sqrtexp (problem 3.4.4)

Details

Time bar (total: 3.3s)

analyze123.0ms (3.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
50%50%50%0%0%0%0%3
50%50%50%0%0%0%0%4
50%50%50%0%0%0%0%5
53.1%53.1%46.9%0%0%0%0%6
54.7%54.7%45.3%0%0%0%0%7
55.5%55.4%44.5%0%0%0%0%8
55.9%55.8%44.1%0%0%0%0%9
56.1%56%43.9%0%0%0%0%10
56.2%56.1%43.8%0%0%0%0%11
56.2%56.2%43.8%0%0%0%0%12
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.2s (67.4%)

Results
1.2s2696×body1024valid
408.0ms3848×body256valid
289.0ms1404×body512valid
205.0ms2717×body256unsamplable
111.0ms276×body2048valid
4.0ms32×body256infinite
Bogosity

preprocess42.0ms (1.3%)

Algorithm
2×egg-herbie
Rules
1382×associate-*r*
1260×associate-/l*
1064×associate-/r*
1038×associate-*l*
904×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413021
535215
6135115
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify42.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1382×associate-*r*
1260×associate-/l*
1064×associate-/r*
1038×associate-*l*
904×fma-def
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413021
535215
6135115
Stop Event
1×node limit
Counts
1 → 5
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval1.0ms (0%)

Compiler

Compiled 41 to 29 computations (29.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New325
Fresh101
Picked000
Done000
Total426
Accurracy
100.0%
Counts
6 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

localize26.0ms (0.8%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(+.f64 1 (exp.f64 x))
Compiler

Compiled 15 to 9 computations (40% saved)

series0.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 1 (exp.f64 x))
0.0ms
x
@-inf
(+.f64 1 (exp.f64 x))
0.0ms
x
@inf
(+.f64 1 (exp.f64 x))

rewrite53.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
1302×pow1
1200×add-exp-log
1200×log1p-expm1-u
1200×expm1-log1p-u
1176×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
113711
2164911
Stop Event
1×node limit
Counts
1 → 30
Calls
Call 1
Inputs
(+.f64 1 (exp.f64 x))
Outputs
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (cbrt.f64 (exp.f64 (+.f64 x x))) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)

simplify56.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1118×distribute-lft-in
1082×distribute-rgt-in
1000×times-frac
802×associate-/l*
516×associate-*r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
085840
1196790
2586616
32851592
Stop Event
1×node limit
Counts
34 → 51
Calls
Call 1
Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (cbrt.f64 (exp.f64 (+.f64 x x))) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
Outputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 x (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) 2)))
(+.f64 x (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) 2)))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(fma.f64 1 (exp.f64 x) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(fma.f64 (cbrt.f64 (exp.f64 (+.f64 x x))) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))

localize31.0ms (0.9%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓99.7%
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
Compiler

Compiled 27 to 7 computations (74.1% saved)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
1.0ms
x
@inf
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
0.0ms
x
@0
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

rewrite62.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
1688×pow1
1566×add-exp-log
1564×log1p-expm1-u
1560×expm1-log1p-u
1532×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
116621
2230221
Stop Event
1×node limit
Counts
1 → 32
Calls
Call 1
Inputs
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
Outputs
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))

simplify58.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
1876×fma-def
990×div-sub
826×log-prod
746×log-div
438×associate-*r/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0110954
1268954
2907954
34654946
Stop Event
1×node limit
Counts
44 → 47
Calls
Call 1
Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
Outputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(fma.f64 (fma.f64 x 1/2 1) x 2)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 x 1/2 1) x 2))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

eval20.0ms (0.6%)

Compiler

Compiled 1161 to 616 computations (46.9% saved)

prune13.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New95398
Fresh000
Picked101
Done101
Total973100
Accurracy
100.0%
Counts
100 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
▶62.6%
(sqrt.f64 (+.f64 2 x))
▶69.5%
(sqrt.f64 2)
Compiler

Compiled 14 to 12 computations (14.3% saved)

localize15.0ms (0.4%)

Compiler

Compiled 5 to 5 computations (0% saved)

localize18.0ms (0.5%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

localize24.0ms (0.7%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(+.f64 2 (expm1.f64 x))
Compiler

Compiled 15 to 9 computations (40% saved)

series0.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 2 (expm1.f64 x))
0.0ms
x
@inf
(+.f64 2 (expm1.f64 x))
0.0ms
x
@-inf
(+.f64 2 (expm1.f64 x))

rewrite61.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
1462×pow1
1358×add-exp-log
1356×log1p-expm1-u
1354×expm1-log1p-u
1336×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114611
2179211
Stop Event
1×node limit
Counts
1 → 32
Calls
Call 1
Inputs
(+.f64 2 (expm1.f64 x))
Outputs
(-.f64 (exp.f64 x) -1)
(-.f64 (+.f64 1 (+.f64 2 (expm1.f64 x))) 1)
(-.f64 (/.f64 4 (-.f64 2 (expm1.f64 x))) (/.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 2 (expm1.f64 x))))
(-.f64 (+.f64 2 (exp.f64 x)) 1)
(*.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 2 (expm1.f64 x)))
(*.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2) (cbrt.f64 (+.f64 2 (expm1.f64 x))))
(*.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) (sqrt.f64 (+.f64 2 (expm1.f64 x))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(*.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (/.f64 1 (-.f64 2 (expm1.f64 x))))
(/.f64 1 (/.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))) (+.f64 (pow.f64 (expm1.f64 x) 3) 8)))
(/.f64 1 (/.f64 (-.f64 2 (expm1.f64 x)) (-.f64 4 (pow.f64 (expm1.f64 x) 2))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 4 (*.f64 2 (expm1.f64 x)))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8)) (neg.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(/.f64 (neg.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (neg.f64 (-.f64 2 (expm1.f64 x))))
(/.f64 (-.f64 (pow.f64 (expm1.f64 x) 2) 4) (-.f64 (expm1.f64 x) 2))
(pow.f64 (+.f64 2 (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) 2)
(sqrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 2 (expm1.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 2 (expm1.f64 x))))
(exp.f64 (log.f64 (+.f64 2 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (+.f64 2 (expm1.f64 x))))
(fma.f64 1 (expm1.f64 x) 2)
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)) 2)
(fma.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)) 2)

simplify56.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
696×associate-+r+
648×associate-*r*
596×associate-*l*
588×fma-neg
566×associate-/r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
094856
1228806
2685806
33679806
Stop Event
1×node limit
Counts
44 → 50
Calls
Call 1
Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(-.f64 (exp.f64 x) -1)
(-.f64 (+.f64 1 (+.f64 2 (expm1.f64 x))) 1)
(-.f64 (/.f64 4 (-.f64 2 (expm1.f64 x))) (/.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 2 (expm1.f64 x))))
(-.f64 (+.f64 2 (exp.f64 x)) 1)
(*.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 2 (expm1.f64 x)))
(*.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2) (cbrt.f64 (+.f64 2 (expm1.f64 x))))
(*.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) (sqrt.f64 (+.f64 2 (expm1.f64 x))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(*.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (/.f64 1 (-.f64 2 (expm1.f64 x))))
(/.f64 1 (/.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))) (+.f64 (pow.f64 (expm1.f64 x) 3) 8)))
(/.f64 1 (/.f64 (-.f64 2 (expm1.f64 x)) (-.f64 4 (pow.f64 (expm1.f64 x) 2))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 4 (*.f64 2 (expm1.f64 x)))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8)) (neg.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(/.f64 (neg.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (neg.f64 (-.f64 2 (expm1.f64 x))))
(/.f64 (-.f64 (pow.f64 (expm1.f64 x) 2) 4) (-.f64 (expm1.f64 x) 2))
(pow.f64 (+.f64 2 (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) 2)
(sqrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 2 (expm1.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 2 (expm1.f64 x))))
(exp.f64 (log.f64 (+.f64 2 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (+.f64 2 (expm1.f64 x))))
(fma.f64 1 (expm1.f64 x) 2)
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)) 2)
(fma.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)) 2)
Outputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(+.f64 x (fma.f64 x (*.f64 x 1/2) 2))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 x (fma.f64 x (*.f64 x 1/2) 2)))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(-.f64 (exp.f64 x) -1)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(-.f64 (+.f64 1 (+.f64 2 (expm1.f64 x))) 1)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(-.f64 (/.f64 4 (-.f64 2 (expm1.f64 x))) (/.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 2 (expm1.f64 x))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(-.f64 (+.f64 2 (exp.f64 x)) 1)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 2 (expm1.f64 x)) 1)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 1 (+.f64 2 (expm1.f64 x)))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 2) (cbrt.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) (sqrt.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (exp.f64 x) -3) 4))
(*.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (/.f64 1 (-.f64 2 (expm1.f64 x))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(/.f64 1 (/.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))) (+.f64 (pow.f64 (expm1.f64 x) 3) 8)))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (exp.f64 x) -3) 4))
(/.f64 1 (/.f64 (-.f64 2 (expm1.f64 x)) (-.f64 4 (pow.f64 (expm1.f64 x) 2))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (exp.f64 x) -3) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (+.f64 (pow.f64 (expm1.f64 x) 2) (-.f64 4 (*.f64 2 (expm1.f64 x)))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (exp.f64 x) -3) 4))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(/.f64 (neg.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8)) (neg.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(*.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (/.f64 1 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) 8) (fma.f64 (expm1.f64 x) (+.f64 (exp.f64 x) -3) 4))
(/.f64 (neg.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (neg.f64 (-.f64 2 (expm1.f64 x))))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(/.f64 (-.f64 (pow.f64 (expm1.f64 x) 2) 4) (-.f64 (expm1.f64 x) 2))
(/.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2)) (-.f64 2 (expm1.f64 x)))
(/.f64 (fma.f64 (expm1.f64 x) (expm1.f64 x) -4) (+.f64 (exp.f64 x) -3))
(/.f64 (+.f64 (pow.f64 (expm1.f64 x) 2) -4) (+.f64 (expm1.f64 x) -2))
(pow.f64 (+.f64 2 (expm1.f64 x)) 1)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 3)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(pow.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3) 1/3)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(pow.f64 (sqrt.f64 (+.f64 2 (expm1.f64 x))) 2)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(sqrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 2))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(log.f64 (exp.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(cbrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 3))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(expm1.f64 (log1p.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(exp.f64 (log.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(log1p.f64 (expm1.f64 (+.f64 2 (expm1.f64 x))))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(fma.f64 1 (expm1.f64 x) 2)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)) 2)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(fma.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)) 2)
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))

eval11.0ms (0.3%)

Compiler

Compiled 554 to 381 computations (31.2% saved)

prune7.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New50050
Fresh000
Picked011
Done022
Total50353
Accurracy
100.0%
Counts
53 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
✓62.6%
(sqrt.f64 (+.f64 2 x))
✓69.5%
(sqrt.f64 2)
Compiler

Compiled 51 to 39 computations (23.5% saved)

regimes18.0ms (0.5%)

Counts
6 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
Calls

3 calls:

10.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
4.0ms
x
2.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Compiler

Compiled 64 to 49 computations (23.4% saved)

regimes4.0ms (0.1%)

Counts
3 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes4.0ms (0.1%)

Accuracy

Total -4.8b remaining (-24.7%)

Threshold costs -4.8b (-24.7%)

Counts
2 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
Outputs
(sqrt.f64 2)
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
69.5%1x
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
2×1-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01335
11735
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Outputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Compiler

Compiled 15 to 13 computations (13.3% saved)

soundness266.0ms (8%)

Rules
1382×associate-*r*
1302×pow1
1260×associate-/l*
1200×add-exp-log
1200×log1p-expm1-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413021
535215
6135115
0711
113711
2164911
085840
1196790
2586616
32851592
Stop Event
1×node limit
1×node limit
1×node limit
Compiler

Compiled 165 to 119 computations (27.9% saved)

end55.0ms (1.7%)

Compiler

Compiled 52 to 44 computations (15.4% saved)

Profiling

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