sqrtexp (problem 3.4.4)

Time bar (total: 5.0s)

start0.0ms (0%)

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

analyze2.0ms (0%)

Memory
2.0MiB live, 2.0MiB 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
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (24.9%)

Memory
48.4MiB live, 918.1MiB allocated; 825ms collecting garbage
Samples
479.0ms8 256×0valid
424.0ms2 620×0exit
Precisions
Click to see histograms. Total time spent on operations: 692.0ms
ival-sqrt: 350.0ms (50.6% of total)
ival-expm1: 132.0ms (19.1% of total)
ival-mult: 114.0ms (16.5% of total)
ival-div: 73.0ms (10.6% of total)
ival-true: 7.0ms (1% of total)
exact: 7.0ms (1% of total)
adjust: 4.0ms (0.6% of total)
ival-assert: 4.0ms (0.6% of total)
Bogosity

explain120.0ms (2.4%)

Memory
25.0MiB live, 126.2MiB allocated; 11ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1740-1(0.007734139480752142)(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1740-0-(-.f64 (exp.f64 x) #s(literal 1 binary64))
00-0-(exp.f64 (*.f64 #s(literal 2 binary64) x))
00-0-#s(literal 1 binary64)
00-0-(*.f64 #s(literal 2 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
00-0-#s(literal 2 binary64)
00-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
00-0-(exp.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (exp.f64 x) #s(literal 1 binary64))cancellation1740
-.f64(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))cancellation1731
Confusion
Predicted +Predicted -
+1710
-382
Precision
0.9827586206896551
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+17100
-3181
Precision?
0.9771428571428571
Recall?
1.0
Freqs
test
numberfreq
082
11
2173
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
39.0ms512×0valid
Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-exp: 7.0ms (28.3% of total)
ival-expm1: 6.0ms (24.3% of total)
ival-mult: 4.0ms (16.2% of total)
ival-div: 3.0ms (12.1% of total)
ival-sqrt: 3.0ms (12.1% of total)
exact: 1.0ms (4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess180.0ms (3.6%)

Memory
-16.1MiB live, 122.2MiB allocated; 15ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01229
13527
28027
325027
4117913
01012
01712
13312
25912
314612
46957
565207
080677
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶33.8%
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify139.0ms (2.8%)

Memory
2.8MiB live, 93.5MiB allocated; 6ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
cost-diff1
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
cost-diff2
(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff2
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
01745
13345
25945
314645
469535
5652035
0806731
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize28.0ms (0.6%)

Memory
-19.3MiB live, 26.1MiB allocated; 3ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy0.02734375
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy40.17467556668105
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy40.19890456916967
(-.f64 (exp.f64 x) #s(literal 1 binary64))
Samples
19.0ms256×0valid
Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-exp: 3.0ms (24.9% of total)
ival-expm1: 3.0ms (24.9% of total)
ival-div: 2.0ms (16.6% of total)
ival-mult: 2.0ms (16.6% of total)
ival-sqrt: 2.0ms (16.6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Counts
4 → 20
Calls
Call 1
Inputs
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms
x
@0
((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms
x
@-inf
((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

simplify193.0ms (3.9%)

Memory
2.2MiB live, 142.8MiB allocated; 46ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077213
1302173
21041172
33429170
08155135
Stop Event
1×iter limit
1×node limit
Counts
20 → 19
Calls
Call 1
Inputs
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp x) 1)
(expm1.f64 x)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

rewrite38.0ms (0.8%)

Memory
36.3MiB live, 36.3MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01033
01733
16519
042315
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
4 → 50
Calls
Call 1
Inputs
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))))))
(/.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64)))))
(expm1.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))))))
(-.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64))
(+.f64 (cosh.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 (sinh.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x))) (*.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (fma.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (exp.f64 x))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))) (*.f64 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64)))) (expm1.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (expm1.f64 x)))
(neg.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 x))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))

eval17.0ms (0.4%)

Memory
-30.3MiB live, 14.0MiB allocated; 9ms collecting garbage
Compiler

Compiled 1 189 to 297 computations (75% saved)

prune6.0ms (0.1%)

Memory
9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New61869
Fresh000
Picked101
Done000
Total62870
Accuracy
100.0%
Counts
70 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
▶100.0%
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
68.1%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶69.6%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
67.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶73.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
68.4%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶69.3%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 274 to 218 computations (20.4% saved)

simplify147.0ms (3%)

Memory
-16.3MiB live, 134.4MiB allocated; 18ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
cost-diff3
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
cost-diff0
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
cost-diff0
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff0
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff0
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
cost-diff0
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff0
(exp.f64 x)
cost-diff0
(+.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
031163
052147
190147
2175147
3485142
41861132
08399132
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(expm1.f64 x)
Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
x
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(expm1.f64 x)

localize65.0ms (1.3%)

Memory
25.0MiB live, 71.0MiB allocated; 3ms collecting garbage
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
accuracy0.0
(expm1.f64 x)
accuracy0.01171875
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
accuracy0.02734375
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.09375
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy0.838886279305326
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy19.615776528486887
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy0.0
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy0.0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy0.01171875
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy19.66264247372277
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy0.01171875
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy17.222129845534077
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy0.0
(exp.f64 x)
accuracy0.01171875
(+.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy0.01171875
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
Samples
46.0ms247×0valid
2.0ms5×2valid
1.0ms4×1valid
Compiler

Compiled 162 to 29 computations (82.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 9.0ms (24.9% of total)
ival-add: 6.0ms (16.6% of total)
ival-sqrt: 6.0ms (16.6% of total)
ival-div: 5.0ms (13.8% of total)
ival-exp: 4.0ms (11.1% of total)
ival-expm1: 4.0ms (11.1% of total)
adjust: 1.0ms (2.8% of total)
exact: 1.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Counts
19 → 46
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(expm1.f64 x)
Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))
2.0ms
x
@inf
((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))
2.0ms
x
@0
((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))

simplify177.0ms (3.6%)

Memory
12.4MiB live, 154.1MiB allocated; 33ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125428
1470359
21558346
36700344
08024291
Stop Event
1×iter limit
1×node limit
Counts
46 → 45
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(*.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)
(* 3/16 (/ x (sqrt 2)))
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp x) 1)
(expm1.f64 x)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)

rewrite195.0ms (3.9%)

Memory
-30.1MiB live, 160.0MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031150
052119
1198119
21173119
08341119
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
19 → 581
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(expm1.f64 x)
Outputs
(*.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
(/.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sinh.f64 (acosh.f64 (exp.f64 x))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (cosh.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (expm1.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 (expm1.f64 x) (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
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(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64))
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(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (neg.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(expm1.f64 (*.f64 x #s(literal 1 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (-.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))

eval108.0ms (2.2%)

Memory
28.5MiB live, 73.3MiB allocated; 5ms collecting garbage
Compiler

Compiled 16 930 to 2 382 computations (85.9% saved)

prune46.0ms (0.9%)

Memory
-17.8MiB live, 48.1MiB allocated; 12ms collecting garbage
Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New5199528
Fresh033
Picked145
Done000
Total52016536
Accuracy
100.0%
Counts
536 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
67.6%
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓100.0%
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
68.1%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
▶69.6%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
67.7%
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
68.1%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓69.6%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶67.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
4.0%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶5.3%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
✓73.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
68.4%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓69.3%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
4.1%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
▶4.5%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
Compiler

Compiled 577 to 433 computations (25% saved)

simplify174.0ms (3.5%)

Memory
-16.8MiB live, 173.3MiB allocated; 24ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff0
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
cost-diff0
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
cost-diff0
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
cost-diff0
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
cost-diff0
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
cost-diff0
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
cost-diff0
(+.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
cost-diff0
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
cost-diff0
(+.f64 x x)
cost-diff0
(expm1.f64 (+.f64 x x))
cost-diff0
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
cost-diff3
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046257
067247
1118247
2238247
3647240
42158226
08710219
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 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)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 3/16 binary64)
Outputs
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 (+.f64 x x))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
x
(expm1.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 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)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 3/16 binary64)

localize111.0ms (2.2%)

Memory
-13.0MiB live, 78.1MiB allocated; 8ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.38681143713269006
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
accuracy0.40625
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy19.615776528486887
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy42.89259828481021
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy0.0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy0.01171875
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy0.01171875
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
accuracy20.17517915043369
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy0.01171875
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
accuracy0.19617416930248222
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
accuracy19.66264247372277
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
accuracy42.8705782030091
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
accuracy0.0
(+.f64 #s(literal 2 binary64) x)
accuracy0.01171875
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy20.490248954411058
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy0.0
(expm1.f64 (+.f64 x x))
accuracy0.0
(expm1.f64 x)
accuracy0.01171875
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
accuracy0.02734375
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
Samples
85.0ms256×0valid
Compiler

Compiled 185 to 36 computations (80.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
ival-mult: 13.0ms (31.3% of total)
ival-add: 9.0ms (21.7% of total)
ival-div: 6.0ms (14.5% of total)
ival-sqrt: 6.0ms (14.5% of total)
ival-expm1: 4.0ms (9.6% of total)
ival-exp: 2.0ms (4.8% of total)
exact: 1.0ms (2.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory
14.4MiB live, 14.4MiB allocated; 0ms collecting garbage
Counts
22 → 45
Calls
Call 1
Inputs
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(expm1.f64 x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
Outputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(* 1/2 (pow x 2))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(+ 1 (* 1/2 x))
(/ x (sqrt 2))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(- (exp (* 2 x)) 1)
(* x (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(- (exp x) 1)
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(- (exp (neg (* -2 x))) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((/ (- (exp (+ x x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (- (exp (+ x x)) 1) (+ x x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (- (exp x) 1) (+ (* 1/2 x) 1) (/ x (sqrt 2)))
3.0ms
x
@inf
((/ (- (exp (+ x x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (- (exp (+ x x)) 1) (+ x x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (- (exp x) 1) (+ (* 1/2 x) 1) (/ x (sqrt 2)))
2.0ms
x
@0
((/ (- (exp (+ x x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (- (exp (+ x x)) 1) (+ x x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (- (exp x) 1) (+ (* 1/2 x) 1) (/ x (sqrt 2)))

simplify161.0ms (3.3%)

Memory
3.9MiB live, 140.4MiB allocated; 23ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0132427
1490366
21640359
37065357
08433293
Stop Event
1×iter limit
1×node limit
Counts
45 → 44
Calls
Call 1
Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(* 1/2 (pow x 2))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(+ 1 (* 1/2 x))
(/ x (sqrt 2))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(- (exp (* 2 x)) 1)
(* x (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(- (exp x) 1)
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(- (exp (neg (* -2 x))) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(*.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) x) x)
(- (exp x) 1)
(expm1.f64 x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) x) x)

rewrite237.0ms (4.8%)

Memory
7.6MiB live, 198.2MiB allocated; 28ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046241
067231
1257210
21575210
09616203
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 521
Calls
Call 1
Inputs
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(expm1.f64 x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
Outputs
(*.f64 (/.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (+.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (*.f64 (+.f64 (sinh.f64 x) #s(literal 1 binary64)) (+.f64 (sinh.f64 x) #s(literal 1 binary64))) (*.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (neg.f64 (/.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (neg.f64 (-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (neg.f64 (+.f64 (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (fabs.f64 (exp.f64 x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (fabs.f64 (exp.f64 x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (*.f64 (+.f64 (fabs.f64 (exp.f64 x)) (-.f64 #s(literal 1 binary64) (fabs.f64 (exp.f64 x)))) (/.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (*.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 (fabs.f64 (exp.f64 x)) (fabs.f64 (exp.f64 x)))) (/.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (expm1.f64 x))))
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(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 x x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x x) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64))) (/.f64 (expm1.f64 x) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64))) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (expm1.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64))) (expm1.f64 x))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (*.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) (-.f64 (sinh.f64 x) #s(literal 1 binary64))) (*.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (fabs.f64 (exp.f64 x)) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (*.f64 (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (pow.f64 (+.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (*.f64 (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (fabs.f64 (exp.f64 x)) (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (fabs.f64 (exp.f64 x)) (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (+.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (fabs.f64 (exp.f64 x))) #s(literal -1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (fabs.f64 (exp.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (-.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) (/.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))) (*.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(/.f64 (fma.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (*.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))) (pow.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))))
(+.f64 (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) (/.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 #s(literal 1 binary64) (*.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 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 x x) #s(literal 2 binary64)))

eval128.0ms (2.6%)

Memory
2.8MiB live, 93.0MiB allocated; 8ms collecting garbage
Compiler

Compiled 15 056 to 2 371 computations (84.3% saved)

prune46.0ms (0.9%)

Memory
-23.0MiB live, 40.7MiB allocated; 15ms collecting garbage
Pruning

16 alts after pruning (8 fresh and 8 done)

PrunedKeptTotal
New5554559
Fresh347
Picked145
Done044
Total55916575
Accuracy
100.0%
Counts
575 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶67.6%
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓100.0%
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶68.1%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
✓69.6%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
▶67.7%
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
▶68.1%
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓69.6%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓67.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
4.0%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓5.3%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
✓73.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶68.4%
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓69.3%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
4.1%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
4.5%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))
Compiler

Compiled 512 to 379 computations (26% saved)

simplify117.0ms (2.4%)

Memory
41.8MiB live, 129.6MiB allocated; 9ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
cost-diff0
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
cost-diff0
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
cost-diff0
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff0
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
cost-diff0
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
cost-diff0
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
cost-diff0
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039291
066291
1104291
2231291
3737282
42891276
08507270
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
x
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
#s(literal 2 binary64)
x
(expm1.f64 x)
Outputs
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
x
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
#s(literal 2 binary64)
x
(expm1.f64 x)

localize129.0ms (2.6%)

Memory
-2.8MiB live, 141.0MiB allocated; 19ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
accuracy0.01171875
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
accuracy0.02734375
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
accuracy20.564591332595715
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
accuracy0.046875
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
accuracy0.0625
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy0.0859375
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy20.091832383768033
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy0.05078125
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy0.0625
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy0.0859375
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy20.288291911197433
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy0.0
(+.f64 #s(literal 1 binary64) x)
accuracy0.01171875
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy0.01171875
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy20.26405391857057
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy0.05859375
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy0.15234375
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy0.75390625
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy20.24023827092429
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
Samples
62.0ms244×0valid
4.0ms5×2valid
4.0ms7×1valid
Compiler

Compiled 224 to 36 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-mult: 15.0ms (29.1% of total)
ival-add: 13.0ms (25.2% of total)
const: 7.0ms (13.6% of total)
ival-sqrt: 5.0ms (9.7% of total)
ival-div: 3.0ms (5.8% of total)
ival-expm1: 3.0ms (5.8% of total)
adjust: 2.0ms (3.9% of total)
ival-exp: 2.0ms (3.9% of total)
exact: 1.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory
-19.4MiB live, 22.6MiB allocated; 9ms collecting garbage
Counts
22 → 69
Calls
Call 1
Inputs
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 1/2 (* 1/6 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
x
(* x (+ 1 (/ 1 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(- (exp (* 2 x)) 1)
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(- (exp (neg (* -2 x))) 1)
Calls

3 calls:

TimeVariablePointExpression
7.0ms
x
@inf
((sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (- (exp (+ x x)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2))
3.0ms
x
@-inf
((sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (- (exp (+ x x)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2))
2.0ms
x
@0
((sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (- (exp (+ x x)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2))

simplify275.0ms (5.5%)

Memory
8.5MiB live, 157.4MiB allocated; 17ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0207751
1753641
22655605
37633603
08436519
Stop Event
1×iter limit
1×node limit
Counts
69 → 68
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 1/2 (* 1/6 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
x
(* x (+ 1 (/ 1 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(- (exp (* 2 x)) 1)
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(- (exp (neg (* -2 x))) 1)
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (*.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1/2 binary64))) x) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) #s(literal -1 binary64) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64)))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))

rewrite280.0ms (5.7%)

Memory
8.1MiB live, 241.7MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
039254
066254
1275227
22106215
08399215
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 1 192
Calls
Call 1
Inputs
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
Outputs
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (neg.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 x) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))) (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))
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(fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 x x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 x x) x)
(fma.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 4 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 4 binary64) x)
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 8 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 8 binary64) (*.f64 #s(literal 2 binary64) x))
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(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64) x)
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(fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x) x)
(fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64) #s(literal 0 binary64))
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(fma.f64 (*.f64 #s(literal 2 binary64) x) x x)
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(fma.f64 #s(literal 2 binary64) (fabs.f64 x) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (fabs.f64 x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) (fabs.f64 x) x)
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) x x)
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 1 binary64) x x)
(fma.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))) x)
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(fma.f64 x #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x))
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(fma.f64 x (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) x)
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 x #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 2 binary64) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 1 binary64) x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(-.f64 (log1p.f64 (pow.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))) (log1p.f64 (-.f64 (pow.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (log1p.f64 (sinh.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)))))
(-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(fabs.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(fabs.f64 (*.f64 #s(literal 2 binary64) x))
(hypot.f64 (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)))
(hypot.f64 (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))))
(hypot.f64 (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(hypot.f64 (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) x))
(hypot.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))) (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))))
(hypot.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(hypot.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) x))
(hypot.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)))
(hypot.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))))
(hypot.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(hypot.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 2 binary64) x))
(hypot.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)))
(hypot.f64 (*.f64 #s(literal 2 binary64) x) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x))))
(hypot.f64 (*.f64 #s(literal 2 binary64) x) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(hypot.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(+.f64 (log.f64 (neg.f64 (exp.f64 x))) (log.f64 (neg.f64 (exp.f64 x))))
(+.f64 (log.f64 (neg.f64 (fabs.f64 (exp.f64 x)))) (log.f64 (neg.f64 (fabs.f64 (exp.f64 x)))))
(+.f64 (cosh.f64 (log.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 (log.f64 (*.f64 #s(literal 2 binary64) x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) x)
(+.f64 x (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3/2 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)))
(log.f64 (fabs.f64 (exp.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) #s(literal 9/256 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))) (*.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))) #s(literal 27/4096 binary64))) (*.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 #s(literal 49/36864 binary64) (*.f64 x x))) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x)))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) #s(literal 9/256 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) #s(literal 9/256 binary64)) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))) (/.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 49/36864 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal -7/192 binary64) x))
(-.f64 #s(literal 3/16 binary64) (*.f64 (neg.f64 x) #s(literal 7/192 binary64)))
(+.f64 (/.f64 (*.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))) (/.f64 #s(literal 27/4096 binary64) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(+.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/36 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))) (*.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))) #s(literal 1/8 binary64))) (*.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/36 binary64) (*.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))) (/.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))
(-.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) #s(literal 1/6 binary64)))
(+.f64 (/.f64 (*.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval248.0ms (5%)

Memory
-34.1MiB live, 179.6MiB allocated; 56ms collecting garbage
Compiler

Compiled 44 981 to 6 370 computations (85.8% saved)

prune42.0ms (0.8%)

Memory
-13.2MiB live, 92.5MiB allocated; 13ms collecting garbage
Pruning

22 alts after pruning (10 fresh and 12 done)

PrunedKeptTotal
New1 29371 300
Fresh033
Picked145
Done088
Total1 294221 316
Accuracy
100.0%
Counts
1 316 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓67.6%
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓100.0%
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓68.1%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
✓69.6%
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
✓67.7%
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓68.1%
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
68.1%
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
2.3%
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
3.7%
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
✓69.6%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓67.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
4.0%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓5.3%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
✓73.7%
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
68.4%
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
68.4%
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
3.0%
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
3.3%
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
✓69.3%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
4.1%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
4.5%
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))
Compiler

Compiled 1 213 to 556 computations (54.2% saved)

regimes30.0ms (0.6%)

Memory
25.4MiB live, 65.4MiB allocated; 10ms collecting garbage
Counts
29 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 #s(approx (- (exp (+ x x)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
Calls

3 calls:

15.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
7.0ms
x
6.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
100.0%1x
Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes22.0ms (0.5%)

Memory
6.9MiB live, 49.7MiB allocated; 7ms collecting garbage
Accuracy

Total -46.2b remaining (-275.1%)

Threshold costs -46.2b (-275.1%)

Counts
23 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))
(sqrt.f64 (+.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (*.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
Outputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
Calls

3 calls:

12.0ms
x
5.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
5.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
73.7%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
73.7%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
73.7%1x
Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify51.0ms (1%)

Memory
-10.0MiB live, 37.6MiB allocated; 2ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01419
13019
25619
314219
468714
5654314
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

derivations153.0ms (3.1%)

Memory
17.6MiB live, 116.0MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077213
1302173
21041172
33429170
08155135
01033
01733
16519
042315
Stop Event
1×fuel
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess22.0ms (0.4%)

Memory
-12.6MiB live, 31.9MiB allocated; 6ms collecting garbage
Compiler

Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...