Details

Time bar (total: 1.6s)

analyze4.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
50%12.5%37.5%5
50%6.2%43.8%6
50%3.1%46.9%7
50%1.6%48.5%8
50%0.8%49.2%9
50%0.4%49.6%10
50.2%0.2%49.6%11
50.2%0.1%49.7%12
50.2%0%49.8%13
50.2%0%49.8%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample844.0ms (54.4%)

Results
831.0ms8256×body128valid
0.0ms1×body128invalid
Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess31.0ms (2%)

Algorithm
2×egg-herbie
Rules
417×times-frac_binary64
412×associate-/l*_binary64
360×associate-/r*_binary64
350×associate-*l*_binary64
200×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
1199
2509
31117
42367
55317
616137
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify20.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
417×times-frac_binary64
412×associate-/l*_binary64
360×associate-/r*_binary64
350×associate-*l*_binary64
200×distribute-rgt-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0711
1199
2509
31117
42367
55317
616137
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(exp.f64 (fma.f64 x x -1))
Compiler

Compiled 25 to 17 computations (32% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(exp.f64 (fma.f64 x x -1))

series1.0ms (0.1%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(exp.f64 (fma.f64 x x -1))
0.0ms
x
@inf
(exp.f64 (fma.f64 x x -1))
0.0ms
x
@-inf
(exp.f64 (fma.f64 x x -1))

rewrite30.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
394×pow1_binary64
361×add-log-exp_binary64
361×log1p-expm1-u_binary64
361×expm1-log1p-u_binary64
353×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1907
29717
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(exp.f64 (fma.f64 x x -1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))))

simplify34.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
724×distribute-lft-out_binary64
385×*-commutative_binary64
380×fma-def_binary64
341×distribute-rgt-out_binary64
340×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02281
15579
213663
344856
4182856
5357856
6458356
Stop Event
1×node limit
Counts
24 → 27
Calls
Call 1
Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (*.f64 x x)))
(*.f64 (+.f64 (*.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x))))
(+.f64 (exp.f64 -1) (fma.f64 (exp.f64 -1) (*.f64 x x) (*.f64 (exp.f64 -1) (*.f64 (pow.f64 x 4) 1/2))))
(*.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1)))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (*.f64 x x) (*.f64 (exp.f64 -1) (*.f64 (pow.f64 x 4) 1/2)))))
(fma.f64 (exp.f64 -1) (*.f64 1/6 (pow.f64 x 6)) (*.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1))))
(*.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (pow.f64 x 6)) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))))
(*.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (fma.f64 1/6 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 4)))))

prune18.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New25227
Fresh000
Picked101
Done000
Total26228
Error
0.0b
Counts
28 → 2
Alt Table
StatusErrorProgram
▶0.0b
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
0.0b
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
Compiler

Compiled 308 to 235 computations (23.7% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(exp.f64 (fma.f64 x x -1))
✓1.0b
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
✓1.0b
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))

series97.0ms (6.3%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
57.0ms
x
@inf
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
37.0ms
x
@-inf
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
2.0ms
x
@0
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
0.0ms
x
@0
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
0.0ms
x
@inf
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))

rewrite34.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
475×pow1_binary64
435×add-log-exp_binary64
435×expm1-log1p-u_binary64
434×log1p-expm1-u_binary64
425×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
110916
2117716
Stop Event
1×node limit
Counts
2 → 38
Calls
Call 1
Inputs
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) 3) 1) (+.f64 (*.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) (+.f64 (exp.f64 (fma.f64 x x -1)) 1)) (+.f64 1 (*.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) (+.f64 (exp.f64 (fma.f64 x x -1)) 1)) 1) (+.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (exp.f64 (fma.f64 x x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))) (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))) (sqrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (exp.f64 (fma.f64 x x -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1)))))))))

simplify32.0ms (2%)

Algorithm
1×egg-herbie
Rules
401×unswap-sqr_binary64
355×fma-neg_binary64
330×times-frac_binary64
238×associate-/l*_binary64
200×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056453
1172442
2589397
33455397
Stop Event
1×node limit
Counts
62 → 55
Calls
Call 1
Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(log.f64 (+.f64 1 (exp.f64 -1)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 1 (exp.f64 -1)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 4)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2))))
(-.f64 (+.f64 (*.f64 1/3 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6)) (pow.f64 (+.f64 1 (exp.f64 -1)) 3))) (+.f64 (*.f64 1/6 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 1 (exp.f64 -1)))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 1 (exp.f64 -1)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 4)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 6)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2)))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (*.f64 x x)))
(*.f64 (+.f64 (*.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x))))
(+.f64 (exp.f64 -1) (fma.f64 (exp.f64 -1) (*.f64 x x) (*.f64 (exp.f64 -1) (*.f64 (pow.f64 x 4) 1/2))))
(*.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (*.f64 x x) (*.f64 (exp.f64 -1) (*.f64 (pow.f64 x 4) 1/2)))))
(fma.f64 (exp.f64 -1) (*.f64 1/6 (pow.f64 x 6)) (*.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(log.f64 (+.f64 1 (exp.f64 -1)))
(log1p.f64 (exp.f64 -1))
(+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))
(+.f64 (log1p.f64 (exp.f64 -1)) (/.f64 (exp.f64 -1) (/.f64 (+.f64 (exp.f64 -1) 1) (*.f64 x x))))
(+.f64 (log1p.f64 (exp.f64 -1)) (*.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x)))
(fma.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x) (log1p.f64 (exp.f64 -1)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 1 (exp.f64 -1)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 4)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2))))
(+.f64 (fma.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 (exp.f64 -1) 1)) (+.f64 (log1p.f64 (exp.f64 -1)) (/.f64 (exp.f64 -1) (/.f64 (+.f64 (exp.f64 -1) 1) (*.f64 x x))))) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 2)) (pow.f64 (+.f64 (exp.f64 -1) 1) 2))))
(fma.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 (exp.f64 -1) 1)) (+.f64 (*.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x)) (-.f64 (log1p.f64 (exp.f64 -1)) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 x 4) (exp.f64 -2)) (pow.f64 (+.f64 (exp.f64 -1) 1) 2))))))
(fma.f64 (/.f64 (exp.f64 -2) (/.f64 (pow.f64 (+.f64 (exp.f64 -1) 1) 2) (pow.f64 x 4))) -1/2 (fma.f64 1/2 (*.f64 (pow.f64 x 4) (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1))) (fma.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x) (log1p.f64 (exp.f64 -1)))))
(-.f64 (+.f64 (*.f64 1/3 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6)) (pow.f64 (+.f64 1 (exp.f64 -1)) 3))) (+.f64 (*.f64 1/6 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 1 (exp.f64 -1)))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 1 (exp.f64 -1)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 -1))) (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 1 (exp.f64 -1))))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 4)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 -1) 2) (pow.f64 x 6)) (pow.f64 (+.f64 1 (exp.f64 -1)) 2)))))
(-.f64 (fma.f64 1/3 (/.f64 (*.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (+.f64 (exp.f64 -1) 1) 3)) (fma.f64 1/6 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 (exp.f64 -1) 1)) (fma.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 (exp.f64 -1) 1)) (+.f64 (log1p.f64 (exp.f64 -1)) (/.f64 (exp.f64 -1) (/.f64 (+.f64 (exp.f64 -1) 1) (*.f64 x x))))))) (*.f64 1/2 (+.f64 (/.f64 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 2)) (pow.f64 (+.f64 (exp.f64 -1) 1) 2)) (/.f64 (*.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 2)) (pow.f64 (+.f64 (exp.f64 -1) 1) 2)))))
(+.f64 (fma.f64 1/3 (/.f64 (pow.f64 x 6) (/.f64 (pow.f64 (+.f64 (exp.f64 -1) 1) 3) (pow.f64 (exp.f64 -1) 3))) (fma.f64 1/6 (*.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (pow.f64 x 6)) (+.f64 (*.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x)) (fma.f64 1/2 (/.f64 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (+.f64 (exp.f64 -1) 1)) (log1p.f64 (exp.f64 -1)))))) (*.f64 -1/2 (+.f64 (/.f64 (*.f64 (pow.f64 x 4) (exp.f64 -2)) (pow.f64 (+.f64 (exp.f64 -1) 1) 2)) (*.f64 (/.f64 (exp.f64 -2) (pow.f64 (+.f64 (exp.f64 -1) 1) 2)) (pow.f64 x 6)))))
(fma.f64 -1/2 (*.f64 (/.f64 (exp.f64 -2) (pow.f64 (+.f64 (exp.f64 -1) 1) 2)) (+.f64 (pow.f64 x 4) (pow.f64 x 6))) (fma.f64 1/6 (*.f64 (pow.f64 x 6) (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1))) (fma.f64 1/3 (*.f64 (/.f64 (pow.f64 x 6) (pow.f64 (+.f64 (exp.f64 -1) 1) 3)) (exp.f64 -3)) (fma.f64 1/2 (*.f64 (pow.f64 x 4) (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1))) (fma.f64 (/.f64 (exp.f64 -1) (+.f64 (exp.f64 -1) 1)) (*.f64 x x) (log1p.f64 (exp.f64 -1)))))))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))
(log.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (exp.f64 (fma.f64 x x -1)))

prune55.0ms (3.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New82082
Fresh011
Picked011
Done000
Total82284
Error
0.0b
Counts
84 → 2
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
▶0.0b
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
Compiler

Compiled 1201 to 981 computations (18.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(exp.f64 (*.f64 x x))
✓0.0b
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))

series2.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
0.0ms
x
@0
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
0.0ms
x
@0
(exp.f64 (*.f64 x x))
0.0ms
x
@-inf
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
0.0ms
x
@inf
(exp.f64 (*.f64 x x))

rewrite33.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
545×pow1_binary64
501×add-log-exp_binary64
501×log1p-expm1-u_binary64
501×expm1-log1p-u_binary64
487×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0715
112913
2142913
Stop Event
1×node limit
Counts
2 → 34
Calls
Call 1
Inputs
(*.f64 (exp.f64 (*.f64 x x)) (exp.f64 -1))
(exp.f64 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3) (pow.f64 (exp.f64 -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (pow.f64 (exp.f64 x) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))))))

simplify32.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
512×fma-def_binary64
439×*-commutative_binary64
437×distribute-rgt-out_binary64
424×associate-*l*_binary64
349×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032244
184216
2208200
3592195
42307195
54558195
Stop Event
1×node limit
Counts
58 → 50
Calls
Call 1
Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (*.f64 x x)))
(*.f64 (fma.f64 x x 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x))))
(+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (fma.f64 x x 1) (exp.f64 -1)))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x)))))
(+.f64 (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))) (*.f64 (fma.f64 x x 1) (exp.f64 -1)))
(fma.f64 (exp.f64 -1) (*.f64 1/6 (pow.f64 x 6)) (*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 4) 1))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 (*.f64 x x) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 x x (*.f64 1/6 (pow.f64 x 6))) (fma.f64 1/2 (pow.f64 x 4) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 4) 1)))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)

prune41.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New48250
Fresh000
Picked101
Done011
Total49352
Error
0.0b
Counts
52 → 3
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
0.1b
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 3) (exp.f64 -1))
▶0.0b
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
Compiler

Compiled 566 to 396 computations (30% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (exp.f64 x) x)
✓0.0b
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

series3.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
1.0ms
x
@inf
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
0.0ms
x
@-inf
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
0.0ms
x
@0
(pow.f64 (exp.f64 x) x)
0.0ms
x
@-inf
(pow.f64 (exp.f64 x) x)

rewrite35.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
575×pow1_binary64
528×add-log-exp_binary64
528×log1p-expm1-u_binary64
528×expm1-log1p-u_binary64
514×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0717
113015
2146815
Stop Event
1×node limit
Counts
2 → 28
Calls
Call 1
Inputs
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(pow.f64 (exp.f64 x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3) (pow.f64 (exp.f64 -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (*.f64 x x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 -1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) (pow.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) 2) (cbrt.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (*.f64 x x))) (sqrt.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 x) (exp.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (*.f64 x x))))))))

simplify33.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
512×fma-def_binary64
439×*-commutative_binary64
437×distribute-rgt-out_binary64
424×associate-*l*_binary64
349×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032244
184216
2208200
3592195
42307195
54558195
Stop Event
1×node limit
Counts
52 → 46
Calls
Call 1
Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (*.f64 x x)))
(*.f64 (fma.f64 x x 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x))))
(+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (fma.f64 x x 1) (exp.f64 -1)))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (exp.f64 -1) (+.f64 (*.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (*.f64 (exp.f64 -1) (*.f64 x x)))))
(+.f64 (fma.f64 1/6 (*.f64 (exp.f64 -1) (pow.f64 x 6)) (*.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))) (*.f64 (fma.f64 x x 1) (exp.f64 -1)))
(fma.f64 (exp.f64 -1) (*.f64 1/6 (pow.f64 x 6)) (*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 4) 1))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 (*.f64 x x) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 x x (*.f64 1/6 (pow.f64 x 6))) (fma.f64 1/2 (pow.f64 x 4) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 4) 1)))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)

prune55.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New46046
Fresh011
Picked011
Done011
Total46349
Error
0.0b
Counts
49 → 3
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
0.1b
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 3) (exp.f64 -1))
✓0.0b
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
Compiler

Compiled 516 to 351 computations (32% saved)

regimes34.0ms (2.2%)

Accuracy

Total 0.0b remaining (53.2%)

Threshold costs 0.0b (53.2%)

Counts
14 → 1
Compiler

Compiled 151 to 102 computations (32.5% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
179
Stop Event
1×saturated
Calls
Call 1
Inputs
(exp.f64 (+.f64 -1 (*.f64 x x)))
Outputs
(exp.f64 (+.f64 -1 (*.f64 x x)))

end58.0ms (3.8%)

Stop Event
1×fuel
Compiler

Compiled 41 to 31 computations (24.4% saved)

Profiling

Loading profile data...