Details

Time bar (total: 2.3s)

analyze137.0ms (6.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.4%24.3%11
31.4%44.3%24.3%12
Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.4s (63.6%)

Results
786.0ms2700×body1024valid
323.0ms3938×body256valid
220.0ms1324×body512valid
101.0ms294×body2048valid
0.0ms1×body256invalid

preprocess19.0ms (0.9%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval0.0ms (0%)

Compiler

Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.3b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶1.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.2b
(/.f64 (exp.f64 x) (expm1.f64 x))
Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite38.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
516×pow1_binary64
493×add-sqr-sqrt_binary64
477×add-log-exp_binary64
477×log1p-expm1-u_binary64
477×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
1998
212878
Stop Event
1×node limit
Counts
1 → 30
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (*.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))))

simplify143.0ms (6.3%)

Algorithm
1×egg-herbie
Rules
1329×sqr-pow_binary64
715×pow-sqr_binary64
530×cube-prod_binary64
472×fabs-mul_binary64
438×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019104
148104
294104
3215104
4331104
5568104
61456104
72283104
82369104
92502104
102660104
112890104
123212104
133633104
144133104
154728104
165448104
175769104
186053104
196277104
206455104
216539104
227479104
Stop Event
1×node limit
Counts
42 → 39
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval7.0ms (0.3%)

Compiler

Compiled 379 to 159 computations (58% saved)

prune7.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New35439
Fresh000
Picked011
Done000
Total35540
Error
1.0b
Counts
40 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓1.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶22.9b
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
▶22.5b
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶22.4b
(+.f64 (/.f64 1 x) 1/2)
▶22.2b
(/.f64 1 x)
Compiler

Compiled 42 to 33 computations (21.4% saved)

localize26.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓0.0b
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓0.1b
(*.f64 -1/720 (pow.f64 x 3))
✓0.3b
(*.f64 1/12 x)
Compiler

Compiled 56 to 43 computations (23.2% saved)

series6.0ms (0.3%)

Counts
4 → 21
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
1.0ms
x
@inf
(*.f64 1/12 x)
1.0ms
x
@0
(*.f64 -1/720 (pow.f64 x 3))
1.0ms
x
@inf
(*.f64 -1/720 (pow.f64 x 3))
1.0ms
x
@-inf
(*.f64 -1/720 (pow.f64 x 3))

rewrite71.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
552×fma-def_binary64
549×log-prod_binary64
320×pow2_binary64
303×fma-neg_binary64
220×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01234
127334
2349834
Stop Event
1×node limit
Counts
4 → 179
Calls
Call 1
Inputs
(*.f64 1/12 x)
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/12 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/12 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 1/1728) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/12 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 1/1728))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/12 x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/518400 (pow.f64 x 6)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/373248000 (pow.f64 x 9)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/518400 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 -1/373248000 (pow.f64 x 9)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log1p.f64 -721/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log1p.f64 -721/720)) 1))))))
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(pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)) (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3))) (neg.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (*.f64 1/12 x) 2)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)) (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 (/.f64 1 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 1 x))))))

simplify144.0ms (6.4%)

Algorithm
1×egg-herbie
Rules
1329×sqr-pow_binary64
715×pow-sqr_binary64
530×cube-prod_binary64
471×fabs-mul_binary64
447×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017198
139198
264198
3128198
4201198
5431198
61303198
72048198
82135198
92268198
102426198
112656198
122978198
133399198
143899198
154494198
165218198
175541198
185825198
196047198
206225198
216305198
227245198
Stop Event
1×node limit
Counts
200 → 190
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(+.f64 (*.f64 1/12 x) (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(/.f64 1 x)
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
Outputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 x (*.f64 x -1/720) 1/12))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 x (*.f64 x -1/720) 1/12))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x))
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))

localize11.0ms (0.5%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
0.3b
(*.f64 1/12 x)
Compiler

Compiled 27 to 20 computations (25.9% saved)

localize5.0ms (0.2%)

Compiler

Compiled 12 to 9 computations (25% saved)

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval121.0ms (5.3%)

Compiler

Compiled 4914 to 3911 computations (20.4% saved)

prune32.0ms (1.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New2650265
Fresh000
Picked011
Done044
Total2655270
Error
1.0b
Counts
270 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓1.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓22.9b
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
✓22.5b
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓22.4b
(+.f64 (/.f64 1 x) 1/2)
✓22.2b
(/.f64 1 x)
Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes12.0ms (0.5%)

Counts
6 → 1
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
Calls

3 calls:

6.0ms
x
2.0ms
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms
(exp.f64 x)
Results
ErrorSegmentsBranch
1.3b1x
1.3b1(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
1.3b1(exp.f64 x)
Compiler

Compiled 58 to 40 computations (31% saved)

regimes5.0ms (0.2%)

Accuracy

Total -1.2b remaining (-5.5%)

Threshold costs -1.2b (-5.5%)

Counts
4 → 1
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
Outputs
(/.f64 1 x)
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
22.2b1x
Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
1912
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 1 x)
Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 1 x)

end19.0ms (0.8%)

Stop Event
1×done
Compiler

Compiled 19 to 13 computations (31.6% saved)

Profiling

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