expax (section 3.5)

Time bar (total: 8.4s)

analyze31.0ms (0.4%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
62.5%62.4%37.5%0.1%0%0%0%5
66.7%62.4%31.2%6.3%0%0%0%6
75.9%68.7%21.9%9.5%0%0%0%7
80%68.7%17.2%14.1%0%0%0%8
86%71.8%11.7%16.5%0%0%0%9
88.9%71.8%9%19.2%0%0%0%10
92.4%73.4%6%20.6%0%0%0%11
94.1%73.4%4.6%22%0%0%0%12
Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-exp: 3.0ms (29.7% of total)
ival-mult: 3.0ms (29.7% of total)
ival-sub: 2.0ms (19.8% of total)
ival->: 1.0ms (9.9% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.5s (17.2%)

Results
968.0ms5362×1valid
205.0ms2894×0valid
20.0ms346×0precondition
Precisions
Click to see histograms. Total time spent on operations: 678.0ms
ival-exp: 299.0ms (44.1% of total)
ival-mult: 134.0ms (19.8% of total)
ival-sub: 93.0ms (13.7% of total)
backward-pass: 79.0ms (11.7% of total)
ival->: 58.0ms (8.6% of total)
const: 15.0ms (2.2% of total)
Bogosity

preprocess28.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
132×sum3-define
96×fma-define
78×fmsub-define
44×sub-neg
40×exp-sum
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01930
14930
27930
311830
417430
522030
628030
738730
841730
944230
1046130
1146230
064
1154
2184
0184
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- (exp (* a x)) 1)
Outputs
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
Call 2
Inputs
(- (exp (* a x)) 1)
(- (exp (* (neg a) x)) 1)
(- (exp (* a (neg x))) 1)
(neg (- (exp (* (neg a) x)) 1))
(neg (- (exp (* a (neg x))) 1))
(- (exp (* x a)) 1)
Outputs
(- (exp (* a x)) 1)
(expm1 (* a x))
(- (exp (* (neg a) x)) 1)
(expm1 (fnmsub a x 0))
(- (exp (* a (neg x))) 1)
(expm1 (fnmsub a x 0))
(neg (- (exp (* (neg a) x)) 1))
(neg (expm1 (fnmsub a x 0)))
(neg (- (exp (* a (neg x))) 1))
(neg (expm1 (fnmsub a x 0)))
(- (exp (* x a)) 1)
(expm1 (* a x))
Symmetry

(sort a x)

explain118.0ms (1.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1390-0-(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
00-0-x
00-0-(*.f64 a x)
00-0-(exp.f64 (*.f64 a x))
00-0-#s(literal 1 binary64)
00-0-a
Results
73.0ms346×1valid
16.0ms166×0valid
Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 37.0ms
ival-exp: 17.0ms (45.3% of total)
ival-mult: 8.0ms (21.3% of total)
backward-pass: 6.0ms (16% of total)
ival-sub: 5.0ms (13.3% of total)
const: 1.0ms (2.7% of total)

eval0.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(expm1.f64 (*.f64 a x))
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 a x)
✓cost-diff0
(expm1.f64 (*.f64 a x))
Rules
6×exp-lowering-exp.f32
6×exp-lowering-exp.f64
4×pow-lowering-pow.f64
4×pow-lowering-pow.f32
4×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1159
2189
0189
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- (exp (* a x)) 1)
(* a x)
a
x
Outputs
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
a
x

localize62.0ms (0.7%)

Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 a x)
✓accuracy100.0%
(expm1.f64 (*.f64 a x))
Results
47.0ms173×5exit
8.0ms83×0valid
Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
backward-pass: 6.0ms (32.9% of total)
ival-mult: 4.0ms (22% of total)
compiled-spec: 4.0ms (22% of total)
ival-exp: 2.0ms (11% of total)
ival-sub: 1.0ms (5.5% of total)
const: 0.0ms (0% of total)

series3.0ms (0%)

Counts
2 → 48
Calls
Call 1
Inputs
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
Outputs
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
Calls

12 calls:

TimeVariablePointExpression
0.0ms
a
@inf
(* a x)
0.0ms
a
@0
(- (exp (* a x)) 1)
0.0ms
x
@0
(- (exp (* a x)) 1)
0.0ms
a
@0
(* a x)
0.0ms
x
@inf
(* a x)

rewrite306.0ms (3.6%)

Algorithm
1×batch-egg-rewrite
Rules
2778×/-lowering-/.f32
2778×/-lowering-/.f64
2514×*-lowering-*.f32
2514×*-lowering-*.f64
1974×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1287
21557
314177
083597
Stop Event
1×iter limit
1×node limit
Counts
2 → 238
Calls
Call 1
Inputs
(- (exp (* a x)) 1)
(* a x)
Outputs
(+.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(+.f64 (expm1.f64 (*.f64 a x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 a x)))
(+.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))))
(+.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a x)) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a x)) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64))))))) (fma.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a x)) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64))))))) (fma.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (exp.f64 (*.f64 a x)) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (exp.f64 (*.f64 a x)) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64))))))) (fma.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))))))
(+.f64 (fma.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (exp.f64 (*.f64 a x)) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64)))))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
(*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (*.f64 (expm1.f64 (*.f64 a x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (*.f64 a x)) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))))
(*.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (*.f64 a x))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64))))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (expm1.f64 (*.f64 a x)))
(*.f64 (+.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (expm1.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (expm1.f64 (*.f64 a x)))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (*.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))) (-.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a x))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(*.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (expm1.f64 (*.f64 a x)))
(*.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 9 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64))))) (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 3 binary64)))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 6 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (+.f64 (exp.f64 (*.f64 (*.f64 a x) #s(literal 4 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(log.f64 (exp.f64 (*.f64 a x)))
(+.f64 (*.f64 a x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 a x))
(+.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) (*.f64 a (/.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) (log.f64 (*.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
(+.f64 (log.f64 (exp.f64 (*.f64 x (/.f64 a #s(literal 2 binary64))))) (log.f64 (exp.f64 (*.f64 x (/.f64 a #s(literal 2 binary64))))))
(+.f64 (log.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))))) (*.f64 a (/.f64 x #s(literal 2 binary64))))
(fma.f64 a x #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(/.f64 (+.f64 (*.f64 (*.f64 a x) (*.f64 (*.f64 a x) (*.f64 a x))) #s(literal 0 binary64)) (+.f64 (*.f64 (*.f64 a x) (*.f64 a x)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 a x) #s(literal 0 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 a x) (*.f64 (*.f64 a x) (*.f64 a x)))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 a x) (*.f64 a x)) (*.f64 #s(literal 0 binary64) (*.f64 a x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) (*.f64 a (/.f64 x #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) (*.f64 a (/.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))) (*.f64 a (/.f64 x #s(literal 2 binary64)))))))
(*.f64 a x)
(*.f64 x a)
(*.f64 #s(literal 2 binary64) (*.f64 a (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) a))
(*.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))) a)
(*.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) a)

simplify238.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
4442×fma-define
3688×fma-lowering-fma.f32
3688×fma-lowering-fma.f64
2334×*-lowering-*.f32
2334×*-lowering-*.f64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
058250
1192238
2604236
31416232
42879232
53199232
63406230
73492230
83506230
93508230
104704230
114704230
124704230
135383230
145849230
156875230
08083230
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
Outputs
(* a x)
(*.f64 a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)

eval34.0ms (0.4%)

Compiler

Compiled 10927 to 740 computations (93.2% saved)

prune35.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2806286
Fresh000
Picked011
Done000
Total2807287
Accuracy
100.0%
Counts
287 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
51.3%
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
▶69.2%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
▶68.3%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
▶61.5%
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
▶68.8%
(*.f64 a x)
✓100.0%
(expm1.f64 (*.f64 a x))
Compiler

Compiled 216 to 130 computations (39.8% saved)

simplify179.0ms (2.1%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))
✓cost-diff0
(+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64)))))))))
✓cost-diff0
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
✓cost-diff256
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64)))))))
✓cost-diff0
(*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))
✓cost-diff0
(*.f64 a x)
✓cost-diff0
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓cost-diff0
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 a x)
✓cost-diff0
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
✓cost-diff0
(*.f64 a x)
✓cost-diff0
(*.f64 x #s(literal 2 binary64))
✓cost-diff0
(*.f64 a (*.f64 x #s(literal 2 binary64)))
✓cost-diff0
(expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
✓cost-diff6912
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
Rules
4472×+-lowering-+.f64
4472×+-lowering-+.f32
2300×*-lowering-*.f32
2300×*-lowering-*.f64
2178×sum3-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
035273
1125256
2448254
31519250
43246250
55418241
08275241
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))
(- (exp (* a (* x 2))) 1)
(* a (* x 2))
a
(* x 2)
x
2
(+ (exp (* a x)) 1)
(exp (* a x))
(* a x)
1
(* a x)
a
x
(* (* a x) (+ 1 (* (* a x) 1/2)))
(* a x)
a
x
(+ 1 (* (* a x) 1/2))
1
(* (* a x) 1/2)
1/2
(* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))
(* a x)
a
x
(+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6))))
1
(* (* a x) (+ 1/2 (* (* a x) 1/6)))
(+ 1/2 (* (* a x) 1/6))
1/2
(* (* a x) 1/6)
1/6
(* a (+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))))
a
(+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))))
x
(* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))
(+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))
(* 1/2 (* x x))
1/2
(* x x)
(* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))
(* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))
(* x (* x x))
(+ 1/6 (* x (* a 1/24)))
1/6
(* x (* a 1/24))
(* a 1/24)
1/24
Outputs
(/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))
(expm1.f64 (*.f64 a x))
(- (exp (* a (* x 2))) 1)
(expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
(* a (* x 2))
(*.f64 a (*.f64 x #s(literal 2 binary64)))
a
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ (exp (* a x)) 1)
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(exp (* a x))
(exp.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
1
#s(literal 1 binary64)
(* a x)
(*.f64 a x)
a
x
(* (* a x) (+ 1 (* (* a x) 1/2)))
(*.f64 x (*.f64 a (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x #s(literal 1/2 binary64))))))
(* a x)
(*.f64 a x)
a
x
(+ 1 (* (* a x) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(* (* a x) 1/2)
(*.f64 a (*.f64 x #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(* a x)
(*.f64 a x)
a
x
(+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6))))
(+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
1
#s(literal 1 binary64)
(* (* a x) (+ 1/2 (* (* a x) 1/6)))
(*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))
(+ 1/2 (* (* a x) 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* (* a x) 1/6)
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* a (+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))))
a
(+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64)))))))))))
x
(* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))
(*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64)))))))))
(+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))
(* 1/2 (* x x))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
(* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))
(*.f64 (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))) (*.f64 a (*.f64 x x)))
(* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))
(* x (* x x))
(*.f64 x (*.f64 x x))
(+ 1/6 (* x (* a 1/24)))
(+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))
1/6
#s(literal 1/6 binary64)
(* x (* a 1/24))
(*.f64 x (*.f64 a #s(literal 1/24 binary64)))
(* a 1/24)
(*.f64 a #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)

localize304.0ms (3.6%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy98.4%
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64)))))))
✓accuracy98.2%
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
✓accuracy94.6%
(*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))
✓accuracy89.8%
(*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))
✓accuracy100.0%
(*.f64 a x)
✓accuracy99.9%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓accuracy99.9%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))
✓accuracy99.6%
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 a x)
✓accuracy100.0%
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
✓accuracy99.8%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
✓accuracy100.0%
(*.f64 a x)
✓accuracy100.0%
(exp.f64 (*.f64 a x))
✓accuracy100.0%
(expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
✓accuracy100.0%
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
✓accuracy99.6%
(*.f64 a (*.f64 x #s(literal 2 binary64)))
Results
196.0ms173×1valid
41.0ms83×0valid
Compiler

Compiled 300 to 35 computations (88.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 130.0ms
ival-mult: 46.0ms (35.3% of total)
ival-add: 20.0ms (15.3% of total)
backward-pass: 17.0ms (13% of total)
compiled-spec: 16.0ms (12.3% of total)
ival-exp: 12.0ms (9.2% of total)
...c/correct-round.rkt:119:19: 12.0ms (9.2% of total)
ival-div: 3.0ms (2.3% of total)
ival-sub: 3.0ms (2.3% of total)
const: 1.0ms (0.8% of total)

series36.0ms (0.4%)

Counts
18 → 420
Calls
Call 1
Inputs
#<alt (/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))>
#<alt (- (exp (* a (* x 2))) 1)>
#<alt (* a (* x 2))>
#<alt (* x 2)>
#<alt (* a x)>
#<alt (* (* a x) (+ 1 (* (* a x) 1/2)))>
#<alt (+ 1 (* (* a x) 1/2))>
#<alt (* (* a x) 1/2)>
#<alt (* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))>
#<alt (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6))))>
#<alt (* (* a x) (+ 1/2 (* (* a x) 1/6)))>
#<alt (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))))>
#<alt (+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))))>
#<alt (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))>
#<alt (exp (* a x))>
#<alt (* (* a x) 1/6)>
#<alt (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))>
Outputs
#<alt (* a x)>
#<alt (* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* a x)>
#<alt (* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* 2 (* a x))>
#<alt (* a (+ (* 2 x) (* 2 (* a (pow x 2)))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (* 2 (* a x))>
#<alt (* x (+ (* 2 a) (* 2 (* (pow a 2) x))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (* 1/2 (* a x))>
#<alt (* a (+ (* 1/2 x) (/ 1 a)))>
#<alt (* a (+ (* 1/2 x) (/ 1 a)))>
#<alt (* a (+ (* 1/2 x) (/ 1 a)))>
#<alt (* 1/2 (* a x))>
#<alt (* -1 (* a (- (* -1/2 x) (/ 1 a))))>
#<alt (* -1 (* a (- (* -1/2 x) (/ 1 a))))>
#<alt (* -1 (* a (- (* -1/2 x) (/ 1 a))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (* 1/2 (* a x))>
#<alt (* x (+ (* 1/2 a) (/ 1 x)))>
#<alt (* x (+ (* 1/2 a) (/ 1 x)))>
#<alt (* x (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (* a x))>
#<alt (* -1 (* x (- (* -1/2 a) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 a) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 a) (/ 1 x))))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))>
#<alt (* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))>
#<alt (* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))>
#<alt (* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))>
#<alt (* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))>
#<alt (+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* a x)))>
#<alt (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))>
#<alt (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))>
#<alt (* 1/2 (* a x))>
#<alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))>
#<alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))>
#<alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))>
#<alt (* 1/2 (* a x))>
#<alt (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))>
#<alt (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))>
#<alt (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* 1/6 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 (* a x))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))>
#<alt (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))>
#<alt (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))>
#<alt (* (pow x 2) (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a (pow x 3)))>
#<alt (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))>
#<alt (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))>
#<alt (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* 1/6 (* a (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))>
#<alt (* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))>
#<alt (* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
Calls

105 calls:

TimeVariablePointExpression
4.0ms
x
@0
(/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))
3.0ms
x
@0
(* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))
1.0ms
x
@inf
(* x 2)
1.0ms
a
@inf
(/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))
1.0ms
a
@-inf
(* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))

rewrite361.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
3690×*-lowering-*.f32
3690×*-lowering-*.f64
2600×/-lowering-/.f32
2600×/-lowering-/.f64
2048×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035196
1224173
22093171
08414171
Stop Event
1×iter limit
1×node limit
Counts
18 → 578
Calls
Call 1
Inputs
(/ (- (exp (* a (* x 2))) 1) (+ (exp (* a x)) 1))
(- (exp (* a (* x 2))) 1)
(* a (* x 2))
(* x 2)
(* a x)
(* (* a x) (+ 1 (* (* a x) 1/2)))
(+ 1 (* (* a x) 1/2))
(* (* a x) 1/2)
(* (* a x) (+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6)))))
(+ 1 (* (* a x) (+ 1/2 (* (* a x) 1/6))))
(* (* a x) (+ 1/2 (* (* a x) 1/6)))
(+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))
(* a (+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))))
(+ x (* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24))))))))
(* a (+ (* 1/2 (* x x)) (* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))))
(exp (* a x))
(* (* a x) 1/6)
(* a (* (* x (* x x)) (+ 1/6 (* x (* a 1/24)))))
Outputs
(+.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(+.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))) #s(literal -1 binary64)))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (*.f64 a x))))) (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (*.f64 a x))))))
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))))
(-.f64 (/.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal 2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))))
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(exp.f64 (*.f64 a x))
(exp.f64 (*.f64 (log.f64 (exp.f64 x)) a))
(pow.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 a) x)
(pow.f64 (exp.f64 a) (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 a) (+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))))
(pow.f64 (exp.f64 (*.f64 a #s(literal 2 binary64))) (/.f64 x #s(literal 2 binary64)))
(pow.f64 (exp.f64 x) a)
(pow.f64 (exp.f64 x) (*.f64 a #s(literal 1 binary64)))
(pow.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 a x))
(pow.f64 (exp.f64 (*.f64 #s(literal 1 binary64) x)) a)
(pow.f64 (exp.f64 (*.f64 #s(literal 1 binary64) a)) x)
(*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(*.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(*.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x (*.f64 a #s(literal 1/6 binary64)))
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (*.f64 a x))
(*.f64 (*.f64 x #s(literal 1/6 binary64)) a)
(*.f64 (*.f64 #s(literal 1/6 binary64) a) x)
(+.f64 (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))))
(+.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))
(+.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)))
(+.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a))
(+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))))
(fma.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a))
(fma.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))
(fma.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)))
(/.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1/216 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 a (*.f64 a a)) #s(literal 1/13824 binary64))))) (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (-.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)))))
(/.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 a x) (*.f64 a x)) #s(literal 1/576 binary64)))) (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1/216 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 a (*.f64 a a)) #s(literal 1/13824 binary64)))))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (-.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 a x) (*.f64 a x)) #s(literal 1/576 binary64))))) (neg.f64 (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))) (-.f64 (*.f64 (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))) (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))))) (*.f64 (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) (*.f64 a (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) (-.f64 (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64))) (*.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a)) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a)) (*.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) a) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) a)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x))))) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x))))) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 (*.f64 (*.f64 a x) #s(literal 1/24 binary64)) (*.f64 a (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 x (*.f64 x x))))))))
(*.f64 a (*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))))
(*.f64 x (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))) a))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))))
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) a))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))) (*.f64 a (*.f64 x (*.f64 x x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))) a)
(*.f64 (*.f64 a (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64))))
(*.f64 (*.f64 a (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 a x) #s(literal 1/24 binary64)))) (*.f64 x (*.f64 x x)))

simplify270.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
5138×*-lowering-*.f32
5138×*-lowering-*.f64
1978×+-lowering-+.f64
1978×+-lowering-+.f32
1458×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04194712
115294198
254774135
082134135
Stop Event
1×iter limit
1×node limit
Counts
420 → 420
Calls
Call 1
Inputs
(* a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(* 2 (* a x))
(* a (+ (* 2 x) (* 2 (* a (pow x 2)))))
(* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(* 2 (* a x))
(* x (+ (* 2 a) (* 2 (* (pow a 2) x))))
(* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* 1/2 (* a x))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(* 1/2 (* a x))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* 1/2 (* a x))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(* 1/2 (* a x))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 (* a x))))
(* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* 1/2 (pow x 2))
(+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))
(+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))
(+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))
(* 1/2 (* a (pow x 2)))
(* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))
(* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* 1/2 (* a (pow x 2)))
(* (pow x 2) (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* (pow x 2) (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* (pow x 2) (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a (pow x 3)))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* 1/6 (* a (pow x 3)))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* 1/24 (* (pow a 2) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
Outputs
(* a x)
(*.f64 a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 a (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))))))))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 a (+.f64 (*.f64 a (+.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))) (*.f64 x #s(literal -1/2 binary64))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/2 binary64))))))))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(* a x)
(*.f64 a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(*.f64 x (+.f64 a (*.f64 x (+.f64 (*.f64 a (*.f64 a #s(literal 1/2 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 a #s(literal -1/2 binary64)))))))))))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(*.f64 x (+.f64 a (*.f64 x (+.f64 (*.f64 a (*.f64 a #s(literal 1/2 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (+.f64 (*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) #s(literal 1/4 binary64)) (*.f64 (*.f64 a (*.f64 a #s(literal -1/2 binary64))) (*.f64 #s(literal 1/4 binary64) (*.f64 a a)))) (*.f64 (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 a #s(literal -1/2 binary64)))))) (*.f64 a #s(literal -1/2 binary64))))) (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 a #s(literal -1/2 binary64))))))))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(* 2 (* a x))
(*.f64 a (*.f64 x #s(literal 2 binary64)))
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(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 a (*.f64 (*.f64 a a) #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 a (*.f64 a #s(literal 1/2 binary64))) (/.f64 a x)) x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* a x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a))) #s(literal 1 binary64))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a))) #s(literal 1 binary64))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(*.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) a)) a)))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(*.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) a)) a)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* a x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(*.f64 (*.f64 x x) (-.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(*.f64 (*.f64 x x) (-.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))
(* 1/2 (* a x))
(*.f64 x (*.f64 a #s(literal 1/2 binary64)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) a)))
(* 1/2 (* a x))
(*.f64 x (*.f64 a #s(literal 1/2 binary64)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(*.f64 a (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64))))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* 1/6 (* (pow a 2) (pow x 2)))
(*.f64 a (*.f64 (*.f64 a (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 a (*.f64 a #s(literal 1/6 binary64))) (/.f64 (*.f64 a #s(literal 1/2 binary64)) x)))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* 1/6 (* a x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 x (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 a #s(literal 1/6 binary64))))))
(* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 x (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 a #s(literal 1/6 binary64))))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 (*.f64 a #s(literal 1/6 binary64)) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 (*.f64 a #s(literal 1/6 binary64)) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 a #s(literal -1/6 binary64)) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 a #s(literal -1/6 binary64)) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))
(+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64))))))
(+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64))))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) a) a))))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) a) a))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(*.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) a)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))) a)))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(*.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) a)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))) a)))
(* a x)
(*.f64 a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(*.f64 a (+.f64 x (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64))))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) a) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (+.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) a) a) (/.f64 (/.f64 x (*.f64 a a)) a)))))
(* 1/24 (* (pow a 4) (pow x 4)))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) a)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))) a)))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(*.f64 (*.f64 (*.f64 a a) (*.f64 a a)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64)) (/.f64 (-.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) (/.f64 x a)) a)) a)))
(* a x)
(*.f64 a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
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(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a (pow x 3)))
(*.f64 a (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(*.f64 a (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 a #s(literal 1/24 binary64)))))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(*.f64 a (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 a #s(literal 1/24 binary64)))))
(* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))
(*.f64 a (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 a #s(literal 1/24 binary64)))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(*.f64 (*.f64 a a) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) a)))
(* 1/6 (* a (pow x 3)))
(*.f64 a (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 a #s(literal 1/6 binary64))))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 a #s(literal 1/6 binary64))))
(* (pow x 3) (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x (*.f64 (*.f64 a a) #s(literal 1/24 binary64))) (*.f64 a #s(literal 1/6 binary64))))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* 1/24 (* (pow a 2) (pow x 4)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 a a) #s(literal 1/24 binary64)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))
(* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (*.f64 (*.f64 a a) #s(literal 1/24 binary64)) (/.f64 (*.f64 a #s(literal 1/6 binary64)) x)))

eval184.0ms (2.2%)

Compiler

Compiled 33569 to 2562 computations (92.4% saved)

prune97.0ms (1.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New121731220
Fresh011
Picked235
Done011
Total121981227
Accuracy
100.0%
Counts
1227 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶51.3%
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
▶68.3%
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
▶69.2%
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
✓69.2%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓68.3%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
▶18.4%
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
✓68.8%
(*.f64 a x)
✓100.0%
(expm1.f64 (*.f64 a x))
Compiler

Compiled 110 to 68 computations (38.2% saved)

simplify172.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 a (*.f64 x #s(literal 2 binary64)))
✓cost-diff0
(exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
✓cost-diff13824
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
✓cost-diff0
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a)
✓cost-diff0
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
✓cost-diff0
(*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
✓cost-diff0
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
✓cost-diff0
(*.f64 a #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x (*.f64 a #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 a x)
✓cost-diff0
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
Rules
3968×fma-define
3256×fma-lowering-fma.f32
3256×fma-lowering-fma.f64
2046×sum3-define
1594×fnmadd-define
Iterations

Useful iterations: 11 (0.0ms)

IterNodesCost
029219
182207
2229199
3630197
41425197
52410197
62837197
73405197
84191192
94739191
106011190
117262181
08123181
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* a x) (* x (* a 1/2)))
(* a x)
a
x
(* x (* a 1/2))
(* a 1/2)
1/2
(* (* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))) a)
(* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6))))))
x
(+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))
1
(* a (* x (+ 1/2 (* (* a x) 1/6))))
a
(* x (+ 1/2 (* (* a x) 1/6)))
(+ 1/2 (* (* a x) 1/6))
1/2
(* (* a x) 1/6)
(* a x)
1/6
(* (* (+ 1 (* (* a x) 1/2)) a) x)
(* (+ 1 (* (* a x) 1/2)) a)
(+ 1 (* (* a x) 1/2))
1
(* (* a x) 1/2)
(* a x)
a
x
1/2
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
(/ (exp (* a (* x 2))) (+ (exp (* a x)) 1))
(exp (* a (* x 2)))
(* a (* x 2))
a
(* x 2)
x
2
(+ (exp (* a x)) 1)
(exp (* a x))
(* a x)
1
(/ 1 (+ (exp (* a x)) 1))
Outputs
(* (* a x) (* x (* a 1/2)))
(*.f64 a (*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x x))))
(* a x)
(*.f64 a x)
a
x
(* x (* a 1/2))
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
(* a 1/2)
(*.f64 a #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))) a)
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
x
(+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 a (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
1
#s(literal 1 binary64)
(* a (* x (+ 1/2 (* (* a x) 1/6))))
(*.f64 x (*.f64 a (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))
a
(* x (+ 1/2 (* (* a x) 1/6)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))
(+ 1/2 (* (* a x) 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* (* a x) 1/6)
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
(* a x)
(*.f64 a x)
1/6
#s(literal 1/6 binary64)
(* (* (+ 1 (* (* a x) 1/2)) a) x)
(*.f64 x (*.f64 a (+.f64 (*.f64 (*.f64 a x) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(* (+ 1 (* (* a x) 1/2)) a)
(*.f64 a (+.f64 (*.f64 (*.f64 a x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (* (* a x) 1/2))
(+.f64 (*.f64 (*.f64 a x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* (* a x) 1/2)
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
(* a x)
(*.f64 a x)
a
x
1/2
#s(literal 1/2 binary64)
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
(expm1.f64 (*.f64 a x))
(/ (exp (* a (* x 2))) (+ (exp (* a x)) 1))
(/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(exp (* a (* x 2)))
(exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
(* a (* x 2))
(*.f64 a (*.f64 x #s(literal 2 binary64)))
a
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ (exp (* a x)) 1)
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(exp (* a x))
(exp.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
1
#s(literal 1 binary64)
(/ 1 (+ (exp (* a x)) 1))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))

localize321.0ms (3.8%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(exp.f64 (*.f64 a x))
✓accuracy100.0%
(exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
✓accuracy99.6%
(*.f64 a (*.f64 x #s(literal 2 binary64)))
✓accuracy51.3%
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 a x)
✓accuracy100.0%
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
✓accuracy99.9%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a)
✓accuracy98.5%
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
✓accuracy99.6%
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
✓accuracy98.5%
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
✓accuracy98.5%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
✓accuracy98.1%
(*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))
✓accuracy100.0%
(*.f64 x (*.f64 a #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 a x)
✓accuracy100.0%
(*.f64 a #s(literal 1/2 binary64))
✓accuracy99.6%
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
Results
144.0ms89×2valid
86.0ms84×1valid
43.0ms83×0valid
Compiler

Compiled 224 to 30 computations (86.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 140.0ms
ival-mult: 57.0ms (40.8% of total)
ival-exp: 30.0ms (21.5% of total)
backward-pass: 21.0ms (15% of total)
ival-add: 11.0ms (7.9% of total)
ival-div: 9.0ms (6.4% of total)
...c/correct-round.rkt:119:19: 8.0ms (5.7% of total)
ival-sub: 2.0ms (1.4% of total)
const: 1.0ms (0.7% of total)

series29.0ms (0.3%)

Counts
18 → 420
Calls
Call 1
Inputs
#<alt (* (* a x) (* x (* a 1/2)))>
#<alt (* a x)>
#<alt (* x (* a 1/2))>
#<alt (* a 1/2)>
#<alt (* (* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))) a)>
#<alt (* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6))))))>
#<alt (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))>
#<alt (* a (* x (+ 1/2 (* (* a x) 1/6))))>
#<alt (* (* (+ 1 (* (* a x) 1/2)) a) x)>
#<alt (* (+ 1 (* (* a x) 1/2)) a)>
#<alt (+ 1 (* (* a x) 1/2))>
#<alt (* (* a x) 1/2)>
#<alt (- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))>
#<alt (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1))>
#<alt (exp (* a (* x 2)))>
#<alt (* a (* x 2))>
#<alt (* (* a x) 1/6)>
#<alt (exp (* a x))>
Outputs
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
#<alt (* 1/2 (* a x))>
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#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt (* 1/6 (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
Calls

105 calls:

TimeVariablePointExpression
7.0ms
a
@0
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
3.0ms
x
@0
(* (* a x) (* x (* a 1/2)))
2.0ms
x
@0
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
1.0ms
x
@-inf
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
1.0ms
a
@inf
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))

rewrite352.0ms (4.2%)

Algorithm
1×batch-egg-rewrite
Rules
3656×*-lowering-*.f32
3656×*-lowering-*.f64
3382×/-lowering-/.f32
3382×/-lowering-/.f64
2366×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029156
1162133
21453128
08865128
Stop Event
1×iter limit
1×node limit
Counts
18 → 525
Calls
Call 1
Inputs
(* (* a x) (* x (* a 1/2)))
(* a x)
(* x (* a 1/2))
(* a 1/2)
(* (* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))) a)
(* x (+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6))))))
(+ 1 (* a (* x (+ 1/2 (* (* a x) 1/6)))))
(* a (* x (+ 1/2 (* (* a x) 1/6))))
(* (* (+ 1 (* (* a x) 1/2)) a) x)
(* (+ 1 (* (* a x) 1/2)) a)
(+ 1 (* (* a x) 1/2))
(* (* a x) 1/2)
(- (/ (exp (* a (* x 2))) (+ (exp (* a x)) 1)) (/ 1 (+ (exp (* a x)) 1)))
(/ (exp (* a (* x 2))) (+ (exp (* a x)) 1))
(exp (* a (* x 2)))
(* a (* x 2))
(* (* a x) 1/6)
(exp (* a x))
Outputs
(*.f64 a (*.f64 (*.f64 a x) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 x (*.f64 a (*.f64 a (*.f64 x #s(literal 1/2 binary64)))))
(*.f64 x (*.f64 (*.f64 a #s(literal 1/2 binary64)) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 a (*.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) (*.f64 a x)))
(*.f64 (*.f64 a #s(literal 1/2 binary64)) (*.f64 a (*.f64 x x)))
(*.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) (*.f64 a x))
(*.f64 (*.f64 (*.f64 a x) (*.f64 a x)) #s(literal 1/2 binary64))
(*.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) a) x)
(*.f64 (*.f64 (*.f64 a x) a) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 (*.f64 a x) (*.f64 a #s(literal 1/2 binary64))) x)
(*.f64 (*.f64 (*.f64 a x) (*.f64 x #s(literal 1/2 binary64))) a)
(*.f64 (*.f64 (*.f64 a (*.f64 x x)) a) #s(literal 1/2 binary64))
(*.f64 (*.f64 a (*.f64 x x)) (*.f64 a #s(literal 1/2 binary64)))
(log.f64 (exp.f64 (*.f64 a x)))
(+.f64 (*.f64 a x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 a x))
(+.f64 (log.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))))) (log.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64))))))
(*.f64 a x)
(*.f64 a (log.f64 (exp.f64 x)))
(*.f64 x a)
(*.f64 a (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x (*.f64 a #s(literal 1/2 binary64)))
(*.f64 (*.f64 a x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(*.f64 (*.f64 a #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) a)
(*.f64 (*.f64 #s(literal 1 binary64) a) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 a #s(literal 1/2 binary64))) x)
(*.f64 a #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) a)
(+.f64 (*.f64 a x) (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 a x) (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a))
(fma.f64 a x (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(fma.f64 a x (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a))
(fma.f64 x a (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(fma.f64 x a (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a))
(/.f64 (+.f64 (*.f64 (*.f64 a (*.f64 a a)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 a x) (*.f64 a x)) (-.f64 (*.f64 (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))) (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) (*.f64 (*.f64 a x) (*.f64 a (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))))))
(/.f64 (+.f64 (*.f64 (*.f64 a (*.f64 a a)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 a x) (*.f64 a x)) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a) (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a)) (*.f64 (*.f64 a x) (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a)))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))
(*.f64 x (*.f64 a (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))) (*.f64 a x))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))) a)
(*.f64 (*.f64 a (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))) x)
(+.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(+.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) (/.f64 (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))) (-.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))))
(fma.f64 a (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))) x) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(fma.f64 x (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) x)
(fma.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(fma.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))) (*.f64 a x) x)
(fma.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) x x)
(fma.f64 (*.f64 a (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) x)
(fma.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) a x)
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))) (*.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) (-.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(/.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) #s(literal 1 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))) (*.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))) (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))) (neg.f64 (-.f64 x (*.f64 (*.f64 a x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))) x)) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))) x)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a)))))
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(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))) a))))
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(/.f64 (neg.f64 (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (pow.f64 (exp.f64 (neg.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64))))) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (expm1.f64 (*.f64 a x)))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (exp.f64 (*.f64 a x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64))))) (/.f64 (exp.f64 (*.f64 a x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))
(*.f64 (/.f64 (exp.f64 (*.f64 a x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (/.f64 (exp.f64 (*.f64 a x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64))))) (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))))
(*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
(exp.f64 (+.f64 (*.f64 a x) (*.f64 a x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (*.f64 a #s(literal 2 binary64)))) x))
(exp.f64 (*.f64 (log.f64 (exp.f64 (*.f64 x #s(literal 2 binary64)))) a))
(exp.f64 (*.f64 a (+.f64 x x)))
(pow.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (*.f64 a x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64)))
(pow.f64 (exp.f64 a) (+.f64 x x))
(pow.f64 (exp.f64 a) (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (*.f64 a #s(literal 2 binary64))) x)
(pow.f64 (exp.f64 (*.f64 a #s(literal 2 binary64))) (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 x) (*.f64 a #s(literal 2 binary64)))
(pow.f64 (exp.f64 x) (*.f64 #s(literal 2 binary64) a))
(pow.f64 (exp.f64 x) (+.f64 a a))
(pow.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) a)
(pow.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 (*.f64 a #s(literal 2 binary64))) #s(literal 1 binary64)) x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 a x))
(*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 (exp.f64 (*.f64 a x)) (exp.f64 (*.f64 a x)))
(*.f64 (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 a (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))))
(*.f64 a (*.f64 x #s(literal 2 binary64)))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(*.f64 x (*.f64 #s(literal 2 binary64) a))
(*.f64 (*.f64 a x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(*.f64 (*.f64 x #s(literal 2 binary64)) a)
(*.f64 (*.f64 a #s(literal 2 binary64)) x)
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x (*.f64 a #s(literal 1/6 binary64)))
(*.f64 (*.f64 a x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (*.f64 a x))
(*.f64 (*.f64 x #s(literal 1/6 binary64)) a)
(*.f64 (*.f64 #s(literal 1/6 binary64) a) x)
(exp.f64 (*.f64 a x))
(exp.f64 (*.f64 (log.f64 (exp.f64 x)) a))
(pow.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 a) x)
(pow.f64 (exp.f64 a) (+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))))
(pow.f64 (exp.f64 (*.f64 a #s(literal 2 binary64))) (/.f64 x #s(literal 2 binary64)))
(pow.f64 (exp.f64 x) a)
(pow.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 a) #s(literal 1 binary64)) x)
(*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(*.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(*.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))))

simplify316.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
5462×*-lowering-*.f32
5462×*-lowering-*.f64
2154×+-lowering-+.f64
2154×+-lowering-+.f32
1600×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03874396
113793816
254603682
085273682
Stop Event
1×iter limit
1×node limit
Counts
420 → 420
Calls
Call 1
Inputs
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
a
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
a
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(* 1/2 (* (pow a 2) x))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* 1/2 (* a x))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(* 1/2 (* a x))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* 1/2 (* a x))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(* 1/2 (* a x))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* a x)
(* a (+ x (* a (- (+ (* -1/8 (pow x 2)) (pow x 2)) (* 1/2 (* x (- x (* 1/4 x))))))))
(* a (+ x (* a (- (+ (* -1/8 (pow x 2)) (+ (* a (- (+ (* -1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))) (+ (* -1/16 (pow x 3)) (* 2/3 (pow x 3)))) (+ (* 1/4 (* (pow x 2) (- x (* 1/4 x)))) (* 1/2 (* x (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x))))))))))) (pow x 2))) (* 1/2 (* x (- x (* 1/4 x))))))))
(* a (+ x (* a (- (+ (* -1/8 (pow x 2)) (+ (* a (- (+ (* -1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))) (+ (* -1/16 (pow x 3)) (+ (* 2/3 (pow x 3)) (* a (- (+ (* -1/2 (* x (+ (* -1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))) (+ (* -1/16 (pow x 3)) (* 1/24 (pow x 3)))))) (+ (* -1/4 (* (pow x 2) (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))) (+ (* -1/48 (pow x 4)) (* 1/3 (pow x 4))))) (+ (* 1/12 (* (pow x 3) (- x (* 1/4 x)))) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/24 (pow x 3)) (+ (* 1/4 (* (pow x 2) (- x (* 1/4 x)))) (* 1/2 (* x (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))))))))))))))) (+ (* 1/4 (* (pow x 2) (- x (* 1/4 x)))) (* 1/2 (* x (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x))))))))))) (pow x 2))) (* 1/2 (* x (- x (* 1/4 x))))))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(* a x)
(* x (+ a (* x (- (+ (* -1/8 (pow a 2)) (pow a 2)) (* 1/2 (* a (- a (* 1/4 a))))))))
(* x (+ a (* x (- (+ (* -1/8 (pow a 2)) (+ (* x (- (+ (* -1/2 (* a (+ (* -1/8 (pow a 2)) (* 1/8 (pow a 2))))) (+ (* -1/16 (pow a 3)) (* 2/3 (pow a 3)))) (+ (* 1/4 (* (pow a 2) (- a (* 1/4 a)))) (* 1/2 (* a (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a))))))))))) (pow a 2))) (* 1/2 (* a (- a (* 1/4 a))))))))
(* x (+ a (* x (- (+ (* -1/8 (pow a 2)) (+ (* x (- (+ (* -1/2 (* a (+ (* -1/8 (pow a 2)) (* 1/8 (pow a 2))))) (+ (* -1/16 (pow a 3)) (+ (* 2/3 (pow a 3)) (* x (- (+ (* -1/2 (* a (+ (* -1/2 (* a (+ (* -1/8 (pow a 2)) (* 1/8 (pow a 2))))) (+ (* -1/16 (pow a 3)) (* 1/24 (pow a 3)))))) (+ (* -1/4 (* (pow a 2) (+ (* -1/8 (pow a 2)) (* 1/8 (pow a 2))))) (+ (* -1/48 (pow a 4)) (* 1/3 (pow a 4))))) (+ (* 1/12 (* (pow a 3) (- a (* 1/4 a)))) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/24 (pow a 3)) (+ (* 1/4 (* (pow a 2) (- a (* 1/4 a)))) (* 1/2 (* a (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))))))))))))))) (+ (* 1/4 (* (pow a 2) (- a (* 1/4 a)))) (* 1/2 (* a (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a))))))))))) (pow a 2))) (* 1/2 (* a (- a (* 1/4 a))))))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
1/2
(+ 1/2 (* a (- x (* 1/4 x))))
(+ 1/2 (* a (- (+ x (* a (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))) (* 1/4 x))))
(+ 1/2 (* a (- (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/24 (pow x 3)) (+ (* 1/4 (* (pow x 2) (- x (* 1/4 x)))) (* 1/2 (* x (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))))))) (pow x 2)) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))) (* 1/4 x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
1/2
(+ 1/2 (* x (- a (* 1/4 a))))
(+ 1/2 (* x (- (+ a (* x (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))) (* 1/4 a))))
(+ 1/2 (* x (- (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/24 (pow a 3)) (+ (* 1/4 (* (pow a 2) (- a (* 1/4 a)))) (* 1/2 (* a (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))))))) (pow a 2)) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))) (* 1/4 a))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* a (+ (* 2 x) (* 2 (* a (pow x 2))))))
(+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))
(+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
(* 1/6 (* a x))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
Outputs
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 a (*.f64 x x))))
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* a x)
(*.f64 a x)
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 (* a x))
(*.f64 #s(literal 1/2 binary64) (*.f64 a x))
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* a x)
(*.f64 a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(*.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a x)) #s(literal 1 binary64))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) a) (*.f64 x (*.f64 a (*.f64 a #s(literal 1/6 binary64)))))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) a) (*.f64 x (*.f64 a (*.f64 a #s(literal 1/6 binary64)))))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(*.f64 (*.f64 a a) (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 a a))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) x)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 a a))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) x)) (/.f64 a (*.f64 x x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 a a))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) x)) (/.f64 a (*.f64 x x))))
(* 1/6 (* (pow a 3) (pow x 3)))
(*.f64 (*.f64 a a) (*.f64 a (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 a (*.f64 a a))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) x)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal -1/6 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) (/.f64 a x)) x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal -1/6 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) (/.f64 a x)) x))))
(* a x)
(*.f64 a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(*.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a x)) #s(literal 1 binary64))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) a) (*.f64 x (*.f64 a (*.f64 a #s(literal 1/6 binary64)))))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
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(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(- (/ (exp (* 2 (* a x))) (+ 1 (exp (* a x)))) (/ 1 (+ 1 (exp (* a x)))))
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* a (- x (* 1/4 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 #s(literal 3/4 binary64) x)))
(+ 1/2 (* a (- (+ x (* a (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))) (* 1/4 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 a (+.f64 (*.f64 a (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -3/4 binary64) x)) (*.f64 (*.f64 x x) #s(literal 7/8 binary64)))) (*.f64 #s(literal 3/4 binary64) x))))
(+ 1/2 (* a (- (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/24 (pow x 3)) (+ (* 1/4 (* (pow x 2) (- x (* 1/4 x)))) (* 1/2 (* x (- (pow x 2) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))))))) (pow x 2)) (+ (* 1/8 (pow x 2)) (* 1/2 (* x (- x (* 1/4 x)))))))) (* 1/4 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 a (+.f64 (*.f64 a (+.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -3/4 binary64) x)) (*.f64 (*.f64 x x) #s(literal 7/8 binary64))) (*.f64 a (+.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/8 binary64)) (*.f64 (*.f64 #s(literal 3/4 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -3/4 binary64) x)) (*.f64 (*.f64 x x) #s(literal 7/8 binary64)))))))) (*.f64 #s(literal 3/4 binary64) x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* x (- a (* 1/4 a))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 #s(literal 3/4 binary64) a)))
(+ 1/2 (* x (- (+ a (* x (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))) (* 1/4 a))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 a a) #s(literal 7/8 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 #s(literal 3/4 binary64) a))))) (*.f64 #s(literal 3/4 binary64) a))))
(+ 1/2 (* x (- (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/24 (pow a 3)) (+ (* 1/4 (* (pow a 2) (- a (* 1/4 a)))) (* 1/2 (* a (- (pow a 2) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))))))) (pow a 2)) (+ (* 1/8 (pow a 2)) (* 1/2 (* a (- a (* 1/4 a)))))))) (* 1/4 a))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 (+.f64 (*.f64 (*.f64 a a) #s(literal 7/8 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 #s(literal 3/4 binary64) a)))) (*.f64 x (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/8 binary64)) (+.f64 (*.f64 (*.f64 a #s(literal -1/2 binary64)) (+.f64 (*.f64 (*.f64 a a) #s(literal 7/8 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 #s(literal 3/4 binary64) a))))) (*.f64 (*.f64 #s(literal 3/4 binary64) a) (*.f64 (*.f64 a a) #s(literal -1/4 binary64)))))))) (*.f64 #s(literal 3/4 binary64) a))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (exp (* 2 (* a x))) (+ 1 (exp (* a x))))
(/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
1
#s(literal 1 binary64)
(+ 1 (* 2 (* a x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(+ 1 (* a (+ (* 2 x) (* 2 (* a (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 2 binary64) (+.f64 a (*.f64 a (*.f64 a x))))))
(+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 a (+.f64 (*.f64 (*.f64 a (*.f64 x (*.f64 x x))) #s(literal 4/3 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)))))))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
1
#s(literal 1 binary64)
(+ 1 (* 2 (* a x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 2 binary64) (+.f64 a (*.f64 a (*.f64 a x))))))
(+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 a #s(literal 2 binary64)) (*.f64 x (+.f64 (*.f64 x (*.f64 (*.f64 a (*.f64 a a)) #s(literal 4/3 binary64))) (*.f64 a (*.f64 a #s(literal 2 binary64))))))))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(exp (* 2 (* a x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 a x)))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 2 (* a x))
(*.f64 #s(literal 2 binary64) (*.f64 a x))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (* a x))
(*.f64 a (*.f64 x #s(literal 1/6 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(+.f64 (*.f64 a x) #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+.f64 (*.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+.f64 (*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) a) (*.f64 x (*.f64 a (*.f64 a #s(literal 1/6 binary64))))))))) #s(literal 1 binary64))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(+.f64 (*.f64 a x) #s(literal 1 binary64))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+.f64 (*.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a x)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+.f64 (*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) a) (*.f64 x (*.f64 a (*.f64 a #s(literal 1/6 binary64))))))))) #s(literal 1 binary64))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))

eval138.0ms (1.6%)

Compiler

Compiled 27158 to 2201 computations (91.9% saved)

prune106.0ms (1.3%)

Pruning

8 alts after pruning (1 fresh and 7 done)

PrunedKeptTotal
New110411105
Fresh000
Picked134
Done044
Total110581113
Accuracy
100.0%
Counts
1113 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
✓68.3%
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
✓69.2%
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
✓69.2%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓68.3%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
✓18.4%
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
✓68.8%
(*.f64 a x)
✓100.0%
(expm1.f64 (*.f64 a x))
Compiler

Compiled 103 to 67 computations (35% saved)

simplify173.0ms (2.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(exp.f64 (*.f64 a x))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
✓cost-diff6784
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
Rules
2434×*-lowering-*.f32
2434×*-lowering-*.f64
2096×+-lowering-+.f64
2096×+-lowering-+.f32
1620×--lowering--.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01358
13058
25357
39757
416541
524240
660340
7338840
0818840
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 1 (/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1)))
1
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
(+ 1 (exp (* a x)))
(exp (* a x))
(* a x)
a
x
(- (exp (* a (* x 2))) 1)
(* a (* x 2))
(* x 2)
2
Outputs
(/ 1 (/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1)))
(expm1.f64 (*.f64 a x))
1
#s(literal 1 binary64)
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
(/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(exp (* a x))
(exp.f64 (*.f64 a x))
(* a x)
(*.f64 a x)
a
x
(- (exp (* a (* x 2))) 1)
(expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
(* a (* x 2))
(*.f64 a (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize115.0ms (1.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))
✓accuracy99.8%
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
✓accuracy99.6%
(*.f64 a (*.f64 x #s(literal 2 binary64)))
✓accuracy98.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
Results
58.0ms140×1valid
26.0ms33×5exit
13.0ms83×0valid
Compiler

Compiled 62 to 13 computations (79% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
compiled-spec: 16.0ms (26.5% of total)
ival-exp: 13.0ms (21.5% of total)
ival-mult: 11.0ms (18.2% of total)
backward-pass: 9.0ms (14.9% of total)
ival-div: 4.0ms (6.6% of total)
ival-add: 2.0ms (3.3% of total)
ival-sub: 2.0ms (3.3% of total)
const: 1.0ms (1.7% of total)

series6.0ms (0.1%)

Counts
6 → 144
Calls
Call 1
Inputs
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))>
#<alt (/ 1 (/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (exp (* a x))>
#<alt (* a (* x 2))>
#<alt (- (exp (* a (* x 2))) 1)>
Outputs
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* a (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* a (- (+ (* 1/4 x) (* a (- (* 1/12 (pow x 2)) (+ (* -1/3 (pow x 2)) (+ (* 1/3 (pow x 2)) (* x (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x))))))))) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* x (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* x (- (+ (* 1/4 a) (* x (- (* 1/12 (pow a 2)) (+ (* -1/3 (pow a 2)) (+ (* 1/3 (pow a 2)) (* a (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a))))))))) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))>
#<alt (* a x)>
#<alt (* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* a x)>
#<alt (* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt 2>
#<alt (+ 2 (* a x))>
#<alt (+ 2 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 2 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt 2>
#<alt (+ 2 (* a x))>
#<alt (+ 2 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 2 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* a (+ (* 2 x) (* 2 (* a (pow x 2)))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (* 2 (* a x))>
#<alt (* x (+ (* 2 a) (* 2 (* (pow a 2) x))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
Calls

36 calls:

TimeVariablePointExpression
1.0ms
a
@-inf
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
1.0ms
x
@inf
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
1.0ms
a
@inf
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
0.0ms
x
@-inf
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
0.0ms
a
@0
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))

rewrite319.0ms (3.8%)

Algorithm
1×batch-egg-rewrite
Rules
2634×*-lowering-*.f32
2634×*-lowering-*.f64
2358×/-lowering-/.f32
2358×/-lowering-/.f64
1606×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01348
16647
247430
3540830
0831830
Stop Event
1×iter limit
1×node limit
Counts
6 → 640
Calls
Call 1
Inputs
(/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1))
(/ 1 (/ (+ 1 (exp (* a x))) (- (exp (* a (* x 2))) 1)))
(+ 1 (exp (* a x)))
(exp (* a x))
(* a (* x 2))
(- (exp (* a (* x 2))) 1)
Outputs
(+.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (exp.f64 (*.f64 a x))))
(+.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (exp.f64 (*.f64 a x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (exp.f64 (*.f64 a x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)))
(+.f64 (*.f64 (exp.f64 (*.f64 a x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(+.f64 (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))) (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))) (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))) (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))))
(+.f64 (*.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))) (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))))
(exp.f64 (*.f64 (log.f64 (expm1.f64 (*.f64 a x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 a x))))
(-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 a x))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 a x))))
(/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 a x))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (neg.f64 (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 a x))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64)))) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64)))) (*.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 a x) #s(literal 3 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (exp.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
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(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (+.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) #s(literal 3 binary64)))))
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))))
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (+.f64 (exp.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) (*.f64 a (*.f64 x #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))))
(/.f64 (*.f64 (+.f64 (exp.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) (*.f64 a (*.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))))
(pow.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) #s(literal 1 binary64)))
(*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (*.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))))
(*.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))) (+.f64 (exp.f64 (*.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) (*.f64 a (*.f64 x #s(literal 4 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))) (-.f64 (exp.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 4 binary64))) (*.f64 a (*.f64 x #s(literal 4 binary64))))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 6 binary64)))))) (-.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))

simplify225.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
4248×*-lowering-*.f32
4248×*-lowering-*.f64
3198×+-lowering-+.f64
3198×+-lowering-+.f32
1278×associate-*r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02241510
17191326
224221264
087161264
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(/ 1 (* a x))
(/ (+ (* -1/2 a) (/ 1 x)) a)
(/ (+ (* a (- (* a (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)
(/ (+ (* a (- (* a (- (+ (* 1/4 x) (* a (- (* 1/12 (pow x 2)) (+ (* -1/3 (pow x 2)) (+ (* 1/3 (pow x 2)) (* x (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x))))))))) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ 1 (* a x))
(/ (+ (* -1/2 x) (/ 1 a)) x)
(/ (+ (* x (- (* x (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)
(/ (+ (* x (- (* x (- (+ (* 1/4 a) (* x (- (* 1/12 (pow a 2)) (+ (* -1/3 (pow a 2)) (+ (* 1/3 (pow a 2)) (* a (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a))))))))) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(* a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
2
(+ 2 (* a x))
(+ 2 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 2 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
2
(+ 2 (* a x))
(+ 2 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 2 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
(+ 1 (exp (* a x)))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* 2 (* a x))
(* a (+ (* 2 x) (* 2 (* a (pow x 2)))))
(* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(* 2 (* a x))
(* x (+ (* 2 a) (* 2 (* (pow a 2) x))))
(* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
(- (exp (* 2 (* a x))) 1)
Outputs
(/ 1 (* a x))
(/.f64 #s(literal 1 binary64) (*.f64 a x))
(/ (+ (* -1/2 a) (/ 1 x)) a)
(/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)
(/ (+ (* a (- (* a (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 a (+.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64)))))) a)
(/ (+ (* a (- (* a (- (+ (* 1/4 x) (* a (- (* 1/12 (pow x 2)) (+ (* -1/3 (pow x 2)) (+ (* 1/3 (pow x 2)) (* x (- (* 1/4 x) (+ (* -1/2 x) (* 2/3 x))))))))) (+ (* -1/2 x) (* 2/3 x)))) 1/2)) (/ 1 x)) a)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 a (+.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 0 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64))))))) a)
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ 1 (* a x))
(/.f64 #s(literal 1 binary64) (*.f64 a x))
(/ (+ (* -1/2 x) (/ 1 a)) x)
(/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)
(/ (+ (* x (- (* x (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) a) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64)))))) x)
(/ (+ (* x (- (* x (- (+ (* 1/4 a) (* x (- (* 1/12 (pow a 2)) (+ (* -1/3 (pow a 2)) (+ (* 1/3 (pow a 2)) (* a (- (* 1/4 a) (+ (* -1/2 a) (* 2/3 a))))))))) (+ (* -1/2 a) (* 2/3 a)))) 1/2)) (/ 1 a)) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) a) (*.f64 x (+.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 0 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64))))))) x)
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(/ (+ 1 (exp (* a x))) (- (exp (* 2 (* a x))) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))))
(* a x)
(*.f64 a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 x (*.f64 x #s(literal 1/2 binary64))) (*.f64 a (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4 binary64))))))))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 x (*.f64 x #s(literal 1/2 binary64))) (*.f64 a (+.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4 binary64))) (*.f64 a (+.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 5/12 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4 binary64))))))))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(* a x)
(*.f64 a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(*.f64 x (+.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) (*.f64 x (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 (*.f64 a (*.f64 a a)) #s(literal -1/4 binary64))))))))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(*.f64 x (+.f64 a (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 a a)) (*.f64 x (+.f64 (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 (*.f64 a (*.f64 a a)) #s(literal -1/4 binary64))) (*.f64 x (+.f64 (*.f64 a (*.f64 a (*.f64 (*.f64 a a) #s(literal 1/8 binary64)))) (*.f64 (*.f64 a #s(literal -1/2 binary64)) (+.f64 (*.f64 (*.f64 a (*.f64 a a)) #s(literal 5/12 binary64)) (*.f64 (*.f64 a (*.f64 a a)) #s(literal -1/4 binary64))))))))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
2
#s(literal 2 binary64)
(+ 2 (* a x))
(+.f64 (*.f64 a x) #s(literal 2 binary64))
(+ 2 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+.f64 #s(literal 2 binary64) (*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x)))
(+ 2 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+.f64 #s(literal 2 binary64) (*.f64 a (+.f64 x (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))))))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
2
#s(literal 2 binary64)
(+ 2 (* a x))
(+.f64 (*.f64 a x) #s(literal 2 binary64))
(+ 2 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+.f64 #s(literal 2 binary64) (*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x)))
(+ 2 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+.f64 #s(literal 2 binary64) (*.f64 a (+.f64 x (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))))))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
(+ 1 (exp (* a x)))
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(+.f64 #s(literal 1 binary64) (*.f64 a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x)))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 x (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))))))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(+.f64 #s(literal 1 binary64) (*.f64 a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 (+.f64 (*.f64 a (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) x)))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 a (+.f64 x (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/6 binary64)))))))))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* a (+ (* 2 x) (* 2 (* a (pow x 2)))))
(*.f64 a (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 a x)) x)))
(* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))
(*.f64 a (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (*.f64 a (*.f64 #s(literal 4/3 binary64) x)))))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))
(*.f64 a (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 a (+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (*.f64 a (*.f64 #s(literal 4/3 binary64) x)))) (*.f64 a (*.f64 a (*.f64 x (*.f64 x (*.f64 #s(literal 2/3 binary64) (*.f64 x x))))))))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(* 2 (* a x))
(*.f64 x (*.f64 a #s(literal 2 binary64)))
(* x (+ (* 2 a) (* 2 (* (pow a 2) x))))
(*.f64 a (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 a x)) x)))
(* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))
(*.f64 a (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 a (*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (*.f64 a (*.f64 #s(literal 4/3 binary64) x)))))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))
(*.f64 x (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 a x)) a)) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 a (*.f64 #s(literal 2/3 binary64) (*.f64 a (*.f64 a a))))) (*.f64 (*.f64 a (*.f64 a a)) #s(literal 4/3 binary64))))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (*.f64 x (*.f64 a #s(literal 2 binary64))))

eval151.0ms (1.8%)

Compiler

Compiled 22902 to 2145 computations (90.6% saved)

prune92.0ms (1.1%)

Pruning

11 alts after pruning (4 fresh and 7 done)

PrunedKeptTotal
New7804784
Fresh000
Picked011
Done167
Total78111792
Accuracy
100.0%
Counts
792 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.6%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 a (+.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64)))))) a))
72.0%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
71.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
✓98.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
67.1%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
✓68.3%
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
✓69.2%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
✓68.3%
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
✓18.4%
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
✓68.8%
(*.f64 a x)
✓100.0%
(expm1.f64 (*.f64 a x))
Compiler

Compiled 341 to 165 computations (51.6% saved)

regimes25.0ms (0.3%)

Counts
16 → 1
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 a (+.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64)))))) a))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(/.f64 (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))) (expm1.f64 (*.f64 a (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 (exp.f64 (*.f64 a (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
Outputs
(expm1.f64 (*.f64 a x))
Calls

5 calls:

7.0ms
x
5.0ms
a
5.0ms
(*.f64 a x)
4.0ms
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
4.0ms
(exp.f64 (*.f64 a x))
Results
AccuracySegmentsBranch
100.0%1a
100.0%1x
100.0%1(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
100.0%1(exp.f64 (*.f64 a x))
100.0%1(*.f64 a x)
Compiler

Compiled 25 to 17 computations (32% saved)

regimes14.0ms (0.2%)

Counts
11 → 2
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 a (+.f64 #s(literal -1/2 binary64) (*.f64 a (*.f64 x #s(literal 1/12 binary64)))))) a))
(*.f64 a (+.f64 x (*.f64 a (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 a (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 a #s(literal 1/24 binary64))))))))))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a)
Calls

3 calls:

6.0ms
x
4.0ms
a
3.0ms
(*.f64 a x)
Results
AccuracySegmentsBranch
72.0%1a
72.0%1x
73.9%2(*.f64 a x)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0%)

Counts
8 → 2
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))
Calls

1 calls:

3.0ms
(*.f64 a x)
Results
AccuracySegmentsBranch
73.9%2(*.f64 a x)
Compiler

Compiled 5 to 3 computations (40% saved)

regimes3.0ms (0%)

Counts
7 → 2
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
Calls

1 calls:

3.0ms
(*.f64 a x)
Results
AccuracySegmentsBranch
73.9%2(*.f64 a x)
Compiler

Compiled 5 to 3 computations (40% saved)

regimes5.0ms (0.1%)

Counts
6 → 2
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
Calls

1 calls:

5.0ms
(*.f64 a x)
Results
AccuracySegmentsBranch
73.9%2(*.f64 a x)
Compiler

Compiled 5 to 3 computations (40% saved)

regimes7.0ms (0.1%)

Accuracy

Total -32.2b remaining (-161.1%)

Threshold costs -32.2b (-161.1%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 a x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))
(*.f64 (*.f64 a x) (*.f64 x (*.f64 a #s(literal 1/2 binary64))))
(*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x)
Outputs
(*.f64 a x)
Calls

3 calls:

2.0ms
x
2.0ms
a
2.0ms
(*.f64 a x)
Results
AccuracySegmentsBranch
68.8%1x
68.8%1a
68.8%1(*.f64 a x)
Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-57944.422243923414
-1.42055298708338e-7
Compiler

Compiled 13 to 10 computations (23.1% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-57944.422243923414
-1.42055298708338e-7
Compiler

Compiled 13 to 10 computations (23.1% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.42055298708338e-7
-2.820866587248166e-9
Compiler

Compiled 13 to 10 computations (23.1% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.42055298708338e-7
-2.820866587248166e-9
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify37.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
26×*-commutative_binary64
12×+-commutative_binary64
2×1-exp_binary64
2×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040131
162131
Stop Event
1×saturated
Calls
Call 1
Inputs
(expm1.f64 (*.f64 a x))
(if (<=.f64 (*.f64 a x) #s(literal -50000 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a))
(if (<=.f64 (*.f64 a x) #s(literal -50000 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x))
(*.f64 a x)
Outputs
(expm1.f64 (*.f64 a x))
(if (<=.f64 (*.f64 a x) #s(literal -50000 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64))))))) a))
(if (<=.f64 (*.f64 a x) #s(literal -50000 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 a (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 a (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))))
(if (<=.f64 (*.f64 a x) #s(literal -50000 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 a x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 a x) #s(literal 1/6 binary64)))))))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)) (*.f64 x (*.f64 a (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))) a) x))
(if (<=.f64 (*.f64 a x) #s(literal -944473296573929/9444732965739290427392 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) a)) (*.f64 x (*.f64 a (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 a x) #s(literal 1/2 binary64))))))
(*.f64 a x)

soundness2.0s (24.2%)

Rules
4442×fma-define
4248×*-lowering-*.f32
4248×*-lowering-*.f64
3690×*-lowering-*.f32
3690×*-lowering-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058250
1192238
2604236
31416232
42879232
53199232
63406230
73492230
83506230
93508230
104704230
114704230
124704230
135383230
145849230
156875230
08083230
064
1154
2184
0184
067
1287
21557
314177
083597
029156
1162133
21453128
08865128
02241510
17191326
224221264
087161264
035196
1224173
22093171
08414171
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×saturated
1×iter limit
1×node limit
Compiler

Compiled 397 to 222 computations (44.1% saved)

preprocess45.0ms (0.5%)

Remove

(sort a x)

Compiler

Compiled 318 to 116 computations (63.5% saved)

end0.0ms (0%)

Profiling

Loading profile data...