Details

Time bar (total: 4.8s)

analyze4.0ms (0.1%)

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
50.4%0.4%49.2%10
50.4%0.2%49.4%11
50.4%0.1%49.5%12
Compiler

Compiled 10 to 8 computations (20% saved)

sample3.4s (70.6%)

Results
2.1s4113×body1024valid
644.0ms1960×body512valid
301.0ms1049×body256valid
256.0ms430×body2048valid
95.0ms550×body128valid
15.0ms154×body64valid
1.0ms6×body64invalid

preprocess50.0ms (1%)

Algorithm
2×egg-herbie
Rules
618×fma-neg_binary64
579×fma-def_binary64
525×cancel-sign-sub-inv_binary64
508×associate-/l*_binary64
425×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11913
23413
35813
412013
526113
671413
7210013
8493912
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify70.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
618×fma-neg_binary64
579×fma-def_binary64
525×cancel-sign-sub-inv_binary64
508×associate-/l*_binary64
425×times-frac_binary64
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
0813
11913
23413
35813
412013
526113
671413
7210013
8493912
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
56.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶56.7b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
Compiler

Compiled 35 to 25 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(exp.f64 (neg.f64 x))
✓6.9b
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series2.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite147.0ms (3.1%)

Algorithm
2×egg-rewrite-iter-limit
2×egg-rewrite
1×batch-egg-rewrite
Rules
277×pow1_binary64
269×add-sqr-sqrt_binary64
263×*-un-lft-identity_binary64
256×add-log-exp_binary64
255×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
113011
2214911
066
11306
221496
066
045
1795
29655
045
Stop Event
1×iter limit
1×node limit
1×iter limit
1×unsound
1×unsound
Counts
2 → 22
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 (neg.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (sinh.f64 x))) (cbrt.f64 (*.f64 2 (sinh.f64 x)))) (cbrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (sinh.f64 x))) (sqrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (sinh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (*.f64 2 (sinh.f64 x)) (*.f64 2 (sinh.f64 x))) (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (sinh.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x)))) (cbrt.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (neg.f64 x))) (sqrt.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (neg.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (neg.f64 x))))))))

simplify51.0ms (1%)

Algorithm
1×egg-herbie
Rules
927×fma-def_binary64
559×cancel-sign-sub-inv_binary64
541×fma-neg_binary64
450×unswap-sqr_binary64
334×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
037158
196156
2229152
3677148
41760147
53859147
67260147
Stop Event
1×node limit
Counts
38 → 40
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (*.f64 1/60 (pow.f64 x 5)))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(exp.f64 (*.f64 -1 x))
(exp.f64 (*.f64 -1 x))
(exp.f64 (*.f64 -1 x))
(exp.f64 (*.f64 -1 x))
Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(*.f64 x (fma.f64 1/3 (*.f64 x x) 2))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 2 x)))
(fma.f64 x (fma.f64 1/3 (*.f64 x x) 2) (*.f64 1/60 (pow.f64 x 5)))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (*.f64 x 1/3) 2) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))
(fma.f64 x (fma.f64 1/3 (*.f64 x x) 2) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 (neg.f64 x) 1)
(-.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x)))
(+.f64 1 (-.f64 (*.f64 1/2 (*.f64 x x)) x))
(fma.f64 1/2 (*.f64 x x) (-.f64 1 x))
(fma.f64 x (fma.f64 x 1/2 -1) 1)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(fma.f64 -1/6 (pow.f64 x 3) (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(+.f64 (-.f64 (*.f64 1/2 (*.f64 x x)) x) (fma.f64 (pow.f64 x 3) -1/6 1))
(-.f64 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 1/2 (*.f64 x x) 1)) x)
(fma.f64 x (fma.f64 x 1/2 -1) (fma.f64 (pow.f64 x 3) -1/6 1))
(-.f64 (fma.f64 (*.f64 x x) (fma.f64 x -1/6 1/2) 1) x)
(exp.f64 (*.f64 -1 x))
(exp.f64 (neg.f64 x))
(exp.f64 (*.f64 -1 x))
(exp.f64 (neg.f64 x))
(exp.f64 (*.f64 -1 x))
(exp.f64 (neg.f64 x))
(exp.f64 (*.f64 -1 x))
(exp.f64 (neg.f64 x))

prune28.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New38240
Fresh000
Picked011
Done000
Total38341
Error
0b
Counts
41 → 3
Alt Table
StatusErrorProgram
✓56.7b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶0.0b
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
0.9b
(/.f64 (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
Compiler

Compiled 561 to 351 computations (37.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sinh.f64 x)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(sinh.f64 x)
1.0ms
x
@inf
(sinh.f64 x)
1.0ms
x
@0
(sinh.f64 x)

rewrite48.0ms (1%)

Algorithm
1×egg-rewrite-iter-limit
1×batch-egg-rewrite
Rules
318×pow1_binary64
311×add-sqr-sqrt_binary64
302×*-un-lft-identity_binary64
297×add-log-exp_binary64
296×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
1633
27853
033
Stop Event
1×iter limit
1×node limit
Counts
1 → 10
Calls
Call 1
Inputs
(sinh.f64 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (sinh.f64 x)) (cbrt.f64 (sinh.f64 x))) (cbrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sinh.f64 x)) (sqrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sinh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sinh.f64 x) (sinh.f64 x)) (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sinh.f64 x)))))))

simplify59.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
872×fma-def_binary64
626×distribute-rgt-neg-in_binary64
624×unswap-sqr_binary64
560×distribute-lft-neg-in_binary64
311×neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025150
167150
2151142
3372142
4686142
51466142
62299142
73552142
84529142
97199142
Stop Event
1×node limit
Counts
22 → 19
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
Outputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(fma.f64 1/6 (pow.f64 x 3) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/5040 (pow.f64 x 7) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

prune17.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New19019
Fresh011
Picked011
Done011
Total19322
Error
0b
Counts
22 → 3
Alt Table
StatusErrorProgram
✓56.7b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓0.0b
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
▶0.9b
(/.f64 (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
Compiler

Compiled 278 to 210 computations (24.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
✓0.0b
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
✓0.1b
(*.f64 1/60 (pow.f64 x 5))
✓0.1b
(*.f64 1/3 (pow.f64 x 3))

series6.0ms (0.1%)

Counts
4 → 9
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 1/3 (pow.f64 x 3))
1.0ms
x
@0
(*.f64 1/3 (pow.f64 x 3))
1.0ms
x
@0
(*.f64 1/60 (pow.f64 x 5))
1.0ms
x
@inf
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
1.0ms
x
@-inf
(*.f64 1/3 (pow.f64 x 3))

rewrite82.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
642×log-prod_binary64
629×fma-def_binary64
374×pow2_binary64
327×fma-neg_binary64
258×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01446
132046
2397146
Stop Event
1×node limit
Counts
4 → 185
Calls
Call 1
Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
(+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log1p.f64 -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log1p.f64 -2/3)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/60 (pow.f64 x 5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/60 (pow.f64 x 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/60 (pow.f64 x 5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/60) (pow.f64 x 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 10) 1/3600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/60 (pow.f64 x 5))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 6) 1/9) (fma.f64 1/3 (pow.f64 x 3) (*.f64 -1/60 (pow.f64 x 5)))) (/.f64 (*.f64 (pow.f64 x 10) 1/3600) (fma.f64 1/3 (pow.f64 x 3) (*.f64 -1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))) 2) (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))) (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 (pow.f64 x 3) 3) 1/27 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 6) 1/9 (*.f64 (pow.f64 x 10) 1/3600)) (*.f64 1/3 (*.f64 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (pow.f64 x 10) 1/3600)) (/.f64 1 (fma.f64 1/3 (pow.f64 x 3) (*.f64 -1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 6) 1/9 (*.f64 (pow.f64 x 10) 1/3600)) (*.f64 1/3 (*.f64 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))) (fma.f64 (pow.f64 (pow.f64 x 3) 3) 1/27 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 -1/60 (pow.f64 x 5))) (-.f64 (*.f64 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(*.f64 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))) (fma.f64 (pow.f64 (pow.f64 x 3) 3) 1/27 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 -1/60 (pow.f64 x 5))) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (pow.f64 x 10) 1/3600))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/3 (pow.f64 x 3)))) (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))) (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/3 (pow.f64 x 3)))) (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5)))) (cbrt.f64 (exp.f64 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60) (+.f64 1 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5)))) (+.f64 1 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 (*.f64 x x) 1/3) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1/3 (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/3 (pow.f64 x 3)) 1 (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5) 1/60 (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/60 (pow.f64 x 5)) 1 (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/60 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x 1/3) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 10)) (*.f64 (cbrt.f64 (pow.f64 x 5)) 1/60) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (cbrt.f64 1/3)) (cbrt.f64 (*.f64 (pow.f64 x 6) 1/9)) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 6) 1/9)) (*.f64 x (cbrt.f64 1/3)) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/60 (pow.f64 x 5))) (cbrt.f64 (*.f64 (pow.f64 x 10) 1/3600)) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 10) 1/3600)) (cbrt.f64 (*.f64 1/60 (pow.f64 x 5))) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/60) (pow.f64 x 5/2)) (*.f64 (sqrt.f64 1/60) (pow.f64 x 5/2)) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (*.f64 (pow.f64 x 3/2) 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(#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))) 1))))))
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1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/60 (cbrt.f64 (pow.f64 x 10))) (cbrt.f64 (pow.f64 x 5)) (fma.f64 1/3 (pow.f64 x 3) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/60 (pow.f64 x 5/2)) (pow.f64 x 5/2) (fma.f64 1/3 (pow.f64 x 3) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (+.f64 x x)))) 1))))))

simplify116.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
1252×sqr-pow_binary64
710×cube-prod_binary64
698×pow-sqr_binary64
678×fabs-mul_binary64
416×unswap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01478
13278
26478
313878
426878
569478
6101278
7164878
8175678
9191878
10213178
11246178
12291778
13351478
14426378
15518978
16569378
17618578
18658578
19690778
20706978
Stop Event
1×node limit
Counts
194 → 192
Calls
Call 1
Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
Outputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 2 x) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(*.f64 x (fma.f64 1/3 (*.f64 x x) 2))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))

prune688.0ms (14.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1920192
Fresh000
Picked011
Done022
Total1923195
Error
0b
Counts
195 → 3
Alt Table
StatusErrorProgram
✓56.7b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓0.0b
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
✓0.9b
(/.f64 (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
Compiler

Compiled 4468 to 3475 computations (22.2% saved)

regimes9.0ms (0.2%)

Accuracy

Total -57.5b remaining (-245436.3%)

Threshold costs -57.5b (-245436.3%)

Counts
3 → 1
Calls
Call 1
Inputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (+.f64 (*.f64 2 x) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
Results
3.0ms0.0bx
2.0ms0.0b(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
2.0ms0.0b(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Compiler

Compiled 50 to 39 computations (22% saved)

simplify2.0ms (0%)

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
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)

end14.0ms (0.3%)

Stop Event
1×done
Compiler

Compiled 14 to 12 computations (14.3% saved)

Profiling

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