Hyperbolic secant

Time bar (total: 3.3s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 10 to 8 computations (20% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
Operation ival-div, time spent: 0.0ms, 0.0% of total-time
Operation ival-exp, time spent: 0.0ms, 0.0% of total-time
Operation ival-add, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

sample1.3s (40.8%)

Results
1.3s8255×256valid
0.0ms1×256valid
Precisions
Click to see histograms. Total time spent on operations: 638.0ms
Operation ival-div, time spent: 398.0ms, 62.0% of total-time
Operation ival-exp, time spent: 137.0ms, 21.0% of total-time
Operation ival-add, time spent: 51.0ms, 8.0% of total-time
Operation ival-neg, time spent: 39.0ms, 6.0% of total-time
Operation const, time spent: 13.0ms, 2.0% of total-time
Bogosity

preprocess214.0ms (6.5%)

Algorithm
1×egg-herbie
Rules
80×fma-neg
80×fma-define
48×sub-neg
28×distribute-lft-neg-in
28×cancel-sign-sub-inv
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
02(176.75702024538995)0-(exp.f64 (neg.f64 x))
00-0-(neg.f64 x)
00-0-(exp.f64 x)
00-0-(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017124
135124
267124
3113124
4170124
5231124
6286124
7302124
8309124
9320124
10332124
11334124
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 #s(literal -2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Symmetry

(abs x)

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
Operation ival-exp, time spent: 10.0ms, 47.0% of total-time
Operation ival-div, time spent: 4.0ms, 19.0% of total-time
Operation ival-add, time spent: 4.0ms, 19.0% of total-time
Operation ival-neg, time spent: 2.0ms, 9.0% of total-time
Operation const, time spent: 1.0ms, 5.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

localize37.0ms (1.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 25 to 9 computations (64% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
Operation ival-exp, time spent: 4.0ms, 43.0% of total-time
Operation ival-div, time spent: 2.0ms, 21.0% of total-time
Operation ival-add, time spent: 2.0ms, 21.0% of total-time
Operation const, time spent: 1.0ms, 11.0% of total-time
Operation ival-neg, time spent: 1.0ms, 11.0% of total-time

series3.0ms (0.1%)

Counts
1 → 8
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))>
Outputs
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/ 2 (+ (exp x) (exp (neg x))))
1.0ms
x
@inf
(/ 2 (+ (exp x) (exp (neg x))))
1.0ms
x
@0
(/ 2 (+ (exp x) (exp (neg x))))

rewrite181.0ms (5.5%)

Algorithm
1×batch-egg-rewrite
Rules
94×associate-*r*
62×add-exp-log
62×add-log-exp
62×log1p-expm1-u
62×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
114420
2234320
Stop Event
1×unsound
Counts
1 → 10
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)

simplify488.0ms (14.7%)

Algorithm
1×egg-herbie
Rules
4772×fma-define
1168×fma-neg
772×distribute-lft-in
528×associate-+l-
500×distribute-rgt-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037256
168240
2136240
3294240
4582240
5929240
61108240
71587240
82418240
93827240
104702240
115157240
125232240
135240240
145240240
155372240
165428240
175428240
187311240
197311240
207311240
217311240
227311240
237313240
Stop Event
1×saturated
Counts
18 → 23
Calls
Call 1
Inputs
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)
Outputs
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -61/720 binary64))) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -61/720 binary64) #s(literal 5/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) (fma.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)

eval5.0ms (0.2%)

Compiler

Compiled 173 to 143 computations (17.3% saved)

prune7.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New18523
Fresh000
Picked011
Done000
Total18624
Accuracy
100.0%
Counts
24 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶47.6%
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
▶47.6%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
▶47.6%
#s(literal 1 binary64)
▶10.5%
#s(literal 1/2 binary64)
▶53.9%
#s(literal 0 binary64)
Compiler

Compiled 65 to 57 computations (12.3% saved)

localize254.0ms (7.7%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓99.9%
(*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
✓99.7%
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 68 to 56 computations (17.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 136.0ms
Operation ival-mult, time spent: 110.0ms, 81.0% of total-time
Operation ival-pow, time spent: 15.0ms, 11.0% of total-time
Operation ival-sub, time spent: 4.0ms, 3.0% of total-time
Operation const, time spent: 4.0ms, 3.0% of total-time
Operation ival-add, time spent: 3.0ms, 2.0% of total-time

series3.0ms (0.1%)

Counts
2 → 9
Calls
Call 1
Inputs
#<alt (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))>
#<alt (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))>
Outputs
#<alt (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
#<alt (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
#<alt (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))>
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(* (pow x 2) (- (* 5/24 (pow x 2)) 1/2))
0.0ms
x
@0
(* 5/24 (pow x 2))
0.0ms
x
@inf
(* 5/24 (pow x 2))
0.0ms
x
@0
(* (pow x 2) (- (* 5/24 (pow x 2)) 1/2))
0.0ms
x
@-inf
(* (pow x 2) (- (* 5/24 (pow x 2)) 1/2))

rewrite78.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
1028×unpow-prod-down
570×log-prod
534×log1p-expm1-u
534×expm1-log1p-u
460×prod-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01249
112849
2151549
Stop Event
1×node limit
Counts
2 → 50
Calls
Call 1
Inputs
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
Outputs
(+.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64)) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))) (sqrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64)))
(log.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(+.f64 (pow.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(+.f64 (pow.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64))) x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(/.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64) #s(literal -1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) #s(literal -1/4 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 2 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))) (sqrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 4 binary64)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 2 binary64)))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))

simplify80.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
1416×fma-define
1094×distribute-lft-in
1006×exp-sum
962×distribute-rgt-in
766×fma-neg
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01572180
12762180
25802180
314062180
443822096
Stop Event
1×node limit
Counts
59 → 69
Calls
Call 1
Inputs
(*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(+.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64)) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))) (sqrt.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64)))
(log.f64 (pow.f64 (exp.f64 #s(literal 5/24 binary64)) (pow.f64 x #s(literal 2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 #s(literal 5/24 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(+.f64 (pow.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal 5/24 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(+.f64 (pow.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal 5/24 binary64))) x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(/.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64) #s(literal -1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) #s(literal -1/4 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 125/13824 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 2 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 25/576 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))) (sqrt.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 4 binary64)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 2 binary64)))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
Outputs
(*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
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(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64))) #s(literal 1/3 binary64)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))) #s(literal 6 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 5/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 5/24 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)))

eval37.0ms (1.1%)

Compiler

Compiled 1209 to 1032 computations (14.6% saved)

prune13.0ms (0.4%)

Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New69069
Fresh000
Picked055
Done011
Total69675
Accuracy
100.0%
Counts
75 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓47.6%
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
✓47.6%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
✓47.6%
#s(literal 1 binary64)
✓10.5%
#s(literal 1/2 binary64)
✓53.9%
#s(literal 0 binary64)
Compiler

Compiled 69 to 59 computations (14.5% saved)

regimes20.0ms (0.6%)

Counts
6 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Calls

3 calls:

16.0ms
x
2.0ms
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
100.0%1(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes7.0ms (0.2%)

Counts
4 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
Outputs
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(literal 0 binary64)
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
99.0%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.2%)

Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
Outputs
#s(literal 1 binary64)
#s(literal 0 binary64)
Calls

1 calls:

6.0ms
x
Results
AccuracySegmentsBranch
98.4%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes21.0ms (0.6%)

Counts
2 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
Outputs
#s(literal 1/2 binary64)
#s(literal 0 binary64)
Calls

1 calls:

21.0ms
x
Results
AccuracySegmentsBranch
61.2%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
Outputs
#s(literal 0 binary64)
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
53.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

bsearch117.0ms (3.5%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
117.0ms
0.11783472558888668
176.75702024538995
Results
15.0ms127×256valid
0.0ms1×256valid
Compiler

Compiled 109 to 98 computations (10.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
Operation ival-exp, time spent: 3.0ms, 52.0% of total-time
Operation ival-div, time spent: 1.0ms, 17.0% of total-time
Operation ival-add, time spent: 1.0ms, 17.0% of total-time
Operation ival-neg, time spent: 1.0ms, 17.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch14.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
176.75702024538995
562.3513582527456
Results
12.0ms79×256valid
0.0ms1×256valid
Compiler

Compiled 43 to 40 computations (7% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
Operation ival-exp, time spent: 2.0ms, 56.0% of total-time
Operation ival-div, time spent: 1.0ms, 28.0% of total-time
Operation ival-add, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

bsearch19.0ms (0.6%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
176.75702024538995
562.3513582527456
Results
17.0ms79×256valid
0.0ms1×256valid
Compiler

Compiled 43 to 40 computations (7% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
Operation ival-exp, time spent: 2.0ms, 55.0% of total-time
Operation ival-div, time spent: 1.0ms, 28.0% of total-time
Operation ival-add, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×+-commutative
4×*-commutative
3×1-exp
2×sub-neg
2×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02995
13995
24195
34295
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1/2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1/2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Compiler

Compiled 38 to 32 computations (15.8% saved)

soundness46.0ms (1.4%)

Rules
94×associate-*r*
62×add-exp-log
62×add-log-exp
62×log1p-expm1-u
62×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
114420
2234320
Stop Event
1×unsound

end0.0ms (0%)

preprocess300.0ms (9.1%)

Remove

(abs x)

Compiler

Compiled 140 to 112 computations (20% saved)

Profiling

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