Details

Time bar (total: 8.0s)

analyze106.0ms (1.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
50%50%50%0%0%0%0%4
62.5%62.5%37.5%0%0%0%0%5
68.8%68.7%31.2%0%0%0%0%6
71.9%71.8%28.1%0%0%0%0%7
73.4%73.4%26.5%0%0%0%0%8
74.2%74.2%25.8%0%0%0%0%9
74.6%74.6%25.4%0%0%0%0%10
74.8%74.8%25.2%0%0%0%0%11
74.9%74.9%25.1%0%0%0%0%12
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.5s (43.7%)

Results
1.6s2600×body1024valid
930.0ms1217×body2048valid
510.0ms3088×body256valid
424.0ms1296×body512valid
43.0ms55×body4096valid
Bogosity

preprocess14.0ms (0.2%)

Algorithm
2×egg-herbie
Rules
2×+-commutative_binary64
1×1-exp_binary64
1×hypot-1-def_binary64
1×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
1139
2149
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x 1))))
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×1-exp_binary64
1×hypot-1-def_binary64
1×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0812
1139
2149
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x 1))))
(log.f64 (+.f64 x (hypot.f64 1 x)))

eval1.0ms (0%)

Compiler

Compiled 16 to 11 computations (31.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
44.1b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶44.1b
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 1 x)
✓0.5b
(+.f64 x (hypot.f64 1 x))
✓1.7b
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

series9.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms
x
@0
(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms
x
@inf
(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms
x
@-inf
(+.f64 x (hypot.f64 1 x))
0.0ms
x
@inf
(+.f64 x (hypot.f64 1 x))

rewrite66.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0620
112120
2155920
Stop Event
1×node limit
Counts
3 → 73
Calls
Call 1
Inputs
(log.f64 (+.f64 x (hypot.f64 1 x)))
(+.f64 x (hypot.f64 1 x))
(hypot.f64 1 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2)) (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (log.f64 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (hypot.f64 1 x))) (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (/.f64 1 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (/.f64 1 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))) (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (hypot.f64 1 x)) (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (+.f64 (+.f64 1 (*.f64 x x)) (-.f64 (*.f64 x x) (*.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (-.f64 x (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (neg.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (neg.f64 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 x x)) (-.f64 (hypot.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2) (cbrt.f64 (hypot.f64 1 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) x)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 x)) (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2) (cbrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 1 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 1 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 1 x)))))))

simplify66.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
455×associate-/r*_binary64
407×associate-*l*_binary64
383×fma-def_binary64
320×+-commutative_binary64
318×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0110560
1332540
2882537
32574537
47619537
Stop Event
1×node limit
Counts
109 → 137
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(*.f64 -1 x)
(-.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
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 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (-.f64 (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4))) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))) (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (log.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 (/.f64 -1/4 x) x))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2))) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))))
(+.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 -5/96 (pow.f64 x 6))))))
(-.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))) (-.f64 (/.f64 -3/32 (pow.f64 x 4)) (log.f64 1/2))))
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 x (fma.f64 (*.f64 x x) 1/2 1))
(+.f64 x (fma.f64 x (*.f64 x 1/2) 1))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x)))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) -1/8 x)))
(+.f64 x (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 1)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 2 x (/.f64 1/2 x))
(fma.f64 x 2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (fma.f64 2 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (fma.f64 2 x (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (/.f64 1/2 x) (-.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/2 x) (/.f64 5/128 (pow.f64 x 7)))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) 1/2))
(fma.f64 (*.f64 x x) 1/2 1)
(fma.f64 x (*.f64 x 1/2) 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) -1/8)))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 (*.f64 (pow.f64 x 4) -1/8)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 1))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -1/8))))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) -1/8 (*.f64 (pow.f64 x 6) 1/16))))
(+.f64 1 (fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (*.f64 x x) 1/2 (*.f64 (pow.f64 x 6) 1/16))))
(+.f64 1 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 (*.f64 (pow.f64 x 6) 1/16))))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(+.f64 x (/.f64 1/2 x))
(-.f64 x (/.f64 -1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 x (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 x (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 x (/.f64 1/16 (pow.f64 x 5))) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/16 (pow.f64 x 5)) (/.f64 1/8 (pow.f64 x 3)))))
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (neg.f64 x) (/.f64 1/2 x))
(fma.f64 x -1 (/.f64 -1/2 x))
(-.f64 (/.f64 -1/2 x) x)
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (neg.f64 x) (/.f64 1/2 x)))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (/.f64 -1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) x))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (neg.f64 x) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (-.f64 (/.f64 -1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 -1/2 x) x) (/.f64 -1/16 (pow.f64 x 5))))

eval43.0ms (0.5%)

Compiler

Compiled 1814 to 1362 computations (24.9% saved)

prune23.0ms (0.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1289137
Fresh000
Picked011
Done000
Total12810138
Error
0.0b
Counts
138 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
▶44.1b
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
▶32.1b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
✓44.1b
(log.f64 (+.f64 x (hypot.f64 1 x)))
31.1b
x
▶46.6b
(log.f64 (*.f64 x 2))
48.5b
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
48.4b
(log.f64 (/.f64 -1/2 x))
▶44.1b
(log.f64 (-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1))
44.4b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶32.4b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
Compiler

Compiled 161 to 126 computations (21.7% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 -1/6 (pow.f64 x 3))
✓0.3b
(*.f64 3/40 (pow.f64 x 5))
✓20.5b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
Compiler

Compiled 42 to 32 computations (23.8% saved)

series5.0ms (0.1%)

Counts
3 → 6
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
1.0ms
x
@0
(*.f64 3/40 (pow.f64 x 5))
1.0ms
x
@0
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
1.0ms
x
@inf
(*.f64 -1/6 (pow.f64 x 3))
0.0ms
x
@0
(*.f64 -1/6 (pow.f64 x 3))

rewrite81.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
556×log-prod_binary64
547×fma-def_binary64
332×pow2_binary64
319×fma-neg_binary64
228×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01229
127929
2351829
Stop Event
1×node limit
Counts
3 → 121
Calls
Call 1
Inputs
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(*.f64 3/40 (pow.f64 x 5))
(*.f64 -1/6 (pow.f64 x 3))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 6) 1/36) (fma.f64 -1/6 (pow.f64 x 3) (neg.f64 (fma.f64 3/40 (pow.f64 x 5) x)))) (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (fma.f64 -1/6 (pow.f64 x 3) (neg.f64 (fma.f64 3/40 (pow.f64 x 5) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))) (pow.f64 (cbrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))) 2) (cbrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))) (sqrt.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 9) -1/216 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 3)) (/.f64 1 (fma.f64 (fma.f64 3/40 (pow.f64 x 5) x) (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (*.f64 -1/6 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/36))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/36) (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2)) (/.f64 1 (fma.f64 -1/6 (pow.f64 x 3) (neg.f64 (fma.f64 3/40 (pow.f64 x 5) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 3/40 (pow.f64 x 5) x) (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (*.f64 -1/6 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/36)) (fma.f64 (pow.f64 x 9) -1/216 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 3))))))) (#(struct:change 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simplify143.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
1204×sqr-pow_binary64
710×cube-prod_binary64
681×fabs-mul_binary64
660×pow-sqr_binary64
416×unswap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01251
13051
26051
313151
426051
571351
6107751
7171951
8182751
9198951
10220251
11253251
12298851
13358651
14433851
15527051
16578051
17627251
18667051
19699051
20715251
Stop Event
1×node limit
Counts
127 → 127
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(*.f64 3/40 (pow.f64 x 5))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 3/40 (pow.f64 x 5)))
(*.f64 3/40 (pow.f64 x 5))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 3/40 (pow.f64 x 5)))
Outputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(*.f64 3/40 (pow.f64 x 5))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 3/40 (pow.f64 x 5)))
(fma.f64 -1/6 (pow.f64 x 3) (*.f64 3/40 (pow.f64 x 5)))
(*.f64 3/40 (pow.f64 x 5))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (*.f64 3/40 (pow.f64 x 5)))
(fma.f64 -1/6 (pow.f64 x 3) (*.f64 3/40 (pow.f64 x 5)))

localize6.0ms (0.1%)

Compiler

Compiled 10 to 7 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.1b
(*.f64 -1/6 (pow.f64 x 3))
Compiler

Compiled 19 to 14 computations (26.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (+.f64 x (hypot.f64 1 x)))
✓0.4b
(-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1)
0.5b
(+.f64 x (hypot.f64 1 x))
✓1.7b
(log.f64 (-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1))
Compiler

Compiled 37 to 27 computations (27% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite78.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
990×pow1_binary64
928×add-log-exp_binary64
926×log1p-expm1-u_binary64
926×expm1-log1p-u_binary64
98×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0838
118526
2276526
Stop Event
1×node limit
Counts
3 → 120
Calls
Call 1
Inputs
(log.f64 (-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1))
(-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1)
(+.f64 1 (+.f64 x (hypot.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2)) (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (log.f64 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) -1)) (log.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) (+.f64 (+.f64 x (hypot.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) -1)) (log1p.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (hypot.f64 1 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (hypot.f64 1 x) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (-.f64 (hypot.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) (+.f64 (+.f64 x (hypot.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (/.f64 1 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) -1) (/.f64 1 (+.f64 (+.f64 x (hypot.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (/.f64 1 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 1) (-.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))) (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (hypot.f64 1 x)) (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) (+.f64 (+.f64 x (hypot.f64 1 x)) 2)) (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) -1) 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/.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (-.f64 x (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (neg.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (neg.f64 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) (+.f64 (+.f64 x (hypot.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2) -1)) (neg.f64 (+.f64 (+.f64 x (hypot.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)) (+.f64 x (-.f64 (hypot.f64 1 x) 1))) (+.f64 x (-.f64 (hypot.f64 1 x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)) (+.f64 x (-.f64 (hypot.f64 1 x) 1)))) (-.f64 1 (+.f64 x (-.f64 (hypot.f64 1 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 x x)) (-.f64 (hypot.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2) (cbrt.f64 (hypot.f64 1 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) x)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 x (hypot.f64 1 x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (+.f64 x (hypot.f64 1 x)))) (/.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (-.f64 1 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (hypot.f64 1 x) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 2) (*.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) (*.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2)) (/.f64 1 (-.f64 1 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 x (hypot.f64 1 x)))) (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (+.f64 x (hypot.f64 1 x))) (-.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3)) (+.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (-.f64 1 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2)) (-.f64 1 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))) (neg.f64 (-.f64 1 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (hypot.f64 1 x) 3)) (+.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 (+.f64 1 x) (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) 1) (+.f64 x (-.f64 (hypot.f64 1 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) (+.f64 1 (*.f64 x x))) (-.f64 (+.f64 1 x) (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3)) 1) (+.f64 1 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2)) 1) (-.f64 1 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (hypot.f64 1 x) (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1)))))

simplify64.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
506×unswap-sqr_binary64
452×associate-/r*_binary64
334×+-commutative_binary64
320×fma-def_binary64
312×associate--l+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0103531
1307512
2828512
32389512
46798512
Stop Event
1×node limit
Counts
156 → 183
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 1 (*.f64 2 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
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 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (-.f64 (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -3/32 (pow.f64 x 4)))))
(-.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 2) (log.f64 x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))) (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (/.f64 -3/32 (pow.f64 x 4)))) (log.f64 x)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (/.f64 -3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 5/96 (pow.f64 x 6)) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 (/.f64 -1 x)) (/.f64 1/4 (*.f64 x x))))
(-.f64 (log.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x))))
(-.f64 (log.f64 (/.f64 -1 x)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 1/2)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (log.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (log.f64 (/.f64 -1 x)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 1/2))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x)))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 1/2) (+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))))))
(+.f64 (/.f64 -1/4 (*.f64 x x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 (/.f64 -1 x))) (-.f64 (log.f64 1/2) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -5/96 (pow.f64 x 6))))))
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 x))
(+.f64 x (fma.f64 (*.f64 x x) 1/2 1))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x)))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) -1/8 x)))
(+.f64 1 (fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (*.f64 x x) 1/2 x)))
(+.f64 1 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 x)))
(fma.f64 (*.f64 x x) 1/2 (+.f64 1 (fma.f64 (pow.f64 x 4) -1/8 x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 2 x (/.f64 1/2 x))
(fma.f64 x 2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (fma.f64 2 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (fma.f64 2 x (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (+.f64 (/.f64 1/2 x) (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5)))) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/8 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/16 (pow.f64 x 5))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (-.f64 (/.f64 5/128 (pow.f64 x 7)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
2
(+.f64 2 x)
(+.f64 x 2)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 2 (fma.f64 (*.f64 x x) 1/2 x))
(+.f64 x (fma.f64 (*.f64 x x) 1/2 2))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x)))
(+.f64 2 (fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) -1/8 x)))
(+.f64 2 (fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (*.f64 x x) 1/2 x)))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 x 2))
(fma.f64 x 2 1)
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x)))
(+.f64 (+.f64 (/.f64 1/2 x) 1) (*.f64 x 2))
(+.f64 1 (fma.f64 x 2 (/.f64 1/2 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (+.f64 (/.f64 1/2 x) 1) (*.f64 x 2)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (+.f64 (fma.f64 x 2 1) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 1 (+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1 (/.f64 1/2 x))
(+.f64 1 (/.f64 -1/2 x))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(+.f64 1 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 -1/2 x)))
(+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 1 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 1 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
(+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 1 (+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/16 (pow.f64 x 5)))))

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
0.0b
(hypot.f64 1 x)
0.5b
(+.f64 x (hypot.f64 1 x))
✓1.7b
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
Compiler

Compiled 39 to 27 computations (30.8% saved)

series5.0ms (0.1%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
1.0ms
x
@inf
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
1.0ms
x
@-inf
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
1.0ms
x
@-inf
(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms
x
@inf
(sqrt.f64 (+.f64 x (hypot.f64 1 x)))

rewrite60.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
694×pow1_binary64
645×add-log-exp_binary64
645×log1p-expm1-u_binary64
645×expm1-log1p-u_binary64
630×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
114120
2178120
Stop Event
1×node limit
Counts
2 → 48
Calls
Call 1
Inputs
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4)) (log.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4) (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 (hypot.f64 1 x) 2))) (sqrt.f64 (-.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (sqrt.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))

simplify129.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
1085×fma-def_binary64
720×sqr-pow_binary64
515×cube-prod_binary64
439×unswap-sqr_binary64
345×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
03295
18595
220595
355689
4142288
5238586
6340886
7364586
8389886
9424286
10475086
11549886
12633686
13717186
14763686
Stop Event
1×node limit
Counts
56 → 62
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -1/12 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5))))
(+.f64 (*.f64 -5/224 (pow.f64 x 7)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5)))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) 1)))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -1/12 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 -1/12 (pow.f64 x 3)))
(fma.f64 -1/12 (pow.f64 x 3) (*.f64 1/2 x))
(*.f64 x (fma.f64 -1/12 (*.f64 x x) 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5))))
(fma.f64 1/2 x (fma.f64 -1/12 (pow.f64 x 3) (*.f64 3/80 (pow.f64 x 5))))
(fma.f64 -1/12 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 3/80 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (*.f64 x -1/12) 1/2) (*.f64 3/80 (pow.f64 x 5)))
(+.f64 (*.f64 -5/224 (pow.f64 x 7)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5)))))
(fma.f64 -5/224 (pow.f64 x 7) (fma.f64 1/2 x (fma.f64 -1/12 (pow.f64 x 3) (*.f64 3/80 (pow.f64 x 5)))))
(fma.f64 1/2 x (fma.f64 -5/224 (pow.f64 x 7) (fma.f64 -1/12 (pow.f64 x 3) (*.f64 3/80 (pow.f64 x 5)))))
(fma.f64 3/80 (pow.f64 x 5) (fma.f64 1/2 x (fma.f64 -5/224 (pow.f64 x 7) (*.f64 -1/12 (pow.f64 x 3)))))
(fma.f64 3/80 (pow.f64 x 5) (fma.f64 -5/224 (pow.f64 x 7) (fma.f64 -1/12 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 -1/12 (pow.f64 x 3) (fma.f64 3/80 (pow.f64 x 5) (fma.f64 -5/224 (pow.f64 x 7) (*.f64 1/2 x))))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) 1))
(fma.f64 x (fma.f64 x 1/8 1/2) 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) 1)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/16 (pow.f64 x 3) 1)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) -1/16 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 3) -1/16 1)))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 (pow.f64 x 3) -1/16 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x -1/16 1/8))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x -1/16 1/8) 1/2) 1)

eval713.0ms (8.9%)

Compiler

Compiled 12960 to 9962 computations (23.1% saved)

prune110.0ms (1.4%)

Pruning

11 alts after pruning (5 fresh and 6 done)

PrunedKeptTotal
New6945699
Fresh404
Picked011
Done055
Total69811709
Error
0b
Counts
709 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
▶44.8b
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))
✓44.1b
(log.f64 (-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1))
▶15.2b
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
✓44.1b
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
✓32.1b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
▶48.4b
(log.f64 (/.f64 -1/2 x))
✓32.4b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶48.5b
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
31.1b
x
✓44.1b
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓46.6b
(log.f64 (*.f64 x 2))
Compiler

Compiled 103 to 80 computations (22.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (/.f64 -1/2 x))
Compiler

Compiled 10 to 7 computations (30% saved)

series58.0ms (0.7%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
24.0ms
x
@0
(log.f64 (/.f64 -1/2 x))
23.0ms
x
@-inf
(log.f64 (/.f64 -1/2 x))
10.0ms
x
@inf
(log.f64 (/.f64 -1/2 x))

rewrite52.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
474×pow1_binary64
465×add-sqr-sqrt_binary64
453×*-un-lft-identity_binary64
443×add-log-exp_binary64
442×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11056
212126
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(log.f64 (/.f64 -1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 -1/2 x)) 2)) (log.f64 (cbrt.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (/.f64 -1/2 x))) (log.f64 (sqrt.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 1/2) (log.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 -1/2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 2) (cbrt.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (/.f64 -1/2 x))) (sqrt.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 -1/2) 3) (pow.f64 (log.f64 x) 3)) (+.f64 (*.f64 (log.f64 -1/2) (log.f64 -1/2)) (+.f64 (*.f64 (log.f64 x) (log.f64 x)) (*.f64 (log.f64 -1/2) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (log.f64 -1/2) (log.f64 -1/2)) (*.f64 (log.f64 x) (log.f64 x))) (+.f64 (log.f64 -1/2) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (/.f64 -1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 -1/2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (/.f64 -1/2 x))))))))

simplify30.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
155×fma-neg_binary64
118×fma-def_binary64
56×cancel-sign-sub-inv_binary64
44×sub-neg_binary64
39×distribute-rgt-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017124
127108
240108
360108
4109108
5204108
6336108
7510108
8658108
9779108
10799108
Stop Event
1×saturated
Counts
37 → 28
Calls
Call 1
Inputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
Outputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 1 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 1 x)
✓0.3b
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
✓1.0b
(-.f64 (hypot.f64 1 x) 1)
✓1.0b
(+.f64 x (-.f64 (hypot.f64 1 x) 1))
Compiler

Compiled 26 to 19 computations (26.9% saved)

series4.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(+.f64 x (-.f64 (hypot.f64 1 x) 1))
0.0ms
x
@0
(-.f64 (hypot.f64 1 x) 1)
0.0ms
x
@0
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
0.0ms
x
@inf
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
0.0ms
x
@-inf
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))

rewrite72.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
847×pow1_binary64
790×add-log-exp_binary64
789×expm1-log1p-u_binary64
788×log1p-expm1-u_binary64
774×add-exp-log_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0729
115629
2215926
Stop Event
1×node limit
Counts
3 → 82
Calls
Call 1
Inputs
(+.f64 x (-.f64 (hypot.f64 1 x) 1))
(-.f64 (hypot.f64 1 x) 1)
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (hypot.f64 1 x) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x (hypot.f64 1 x)) 1)) (/.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (+.f64 (-.f64 x (hypot.f64 1 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (/.f64 1 (fma.f64 x x (*.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (/.f64 1 (+.f64 (-.f64 x (hypot.f64 1 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 x (hypot.f64 1 x)) 1) (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (fma.f64 x x (*.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))) (neg.f64 (+.f64 (-.f64 x (hypot.f64 1 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) 1) (+.f64 (*.f64 (+.f64 x (hypot.f64 1 x)) (+.f64 x (hypot.f64 1 x))) (+.f64 1 (*.f64 (+.f64 x (hypot.f64 1 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 x (hypot.f64 1 x)) (+.f64 x (hypot.f64 1 x))) 1) (+.f64 (+.f64 x (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (*.f64 x x)) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (hypot.f64 1 x) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2) (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 (hypot.f64 1 x) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2) (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) -1) (/.f64 1 (+.f64 (pow.f64 (hypot.f64 1 x) 2) (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) -1) (/.f64 1 (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (hypot.f64 1 x)) 1) (-.f64 (sqrt.f64 (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) (+.f64 1 (hypot.f64 1 x))) (+.f64 (pow.f64 (hypot.f64 1 x) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (hypot.f64 1 x)) (+.f64 (pow.f64 (hypot.f64 1 x) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) -1) (+.f64 (pow.f64 (hypot.f64 1 x) 2) (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) -1) (+.f64 (pow.f64 (hypot.f64 1 x) 2) (-.f64 1 (*.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) -1) (+.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) -1) (-.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) -1)) (neg.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 2) -1)) (neg.f64 (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (hypot.f64 1 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2) (cbrt.f64 (hypot.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) -1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 x (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))))))

simplify53.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
641×associate-*l*_binary64
483×associate-*r*_binary64
415×associate-/r*_binary64
368×fma-def_binary64
338×associate--l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0106525
1316507
2879505
32698505
Stop Event
1×node limit
Counts
118 → 147
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4)))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) (*.f64 -5/128 (pow.f64 x 8)))))
x
(-.f64 x 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(*.f64 -1 x)
(-.f64 (*.f64 -1 x) 1)
(-.f64 (*.f64 -1 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 1)
(fma.f64 2 x -1)
(fma.f64 x 2 -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(+.f64 (/.f64 1/2 x) (fma.f64 2 x -1))
(+.f64 (fma.f64 x 2 -1) (/.f64 1/2 x))
(fma.f64 x 2 (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 2 x -1)) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (fma.f64 x 2 (/.f64 1/2 x)) (+.f64 1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 -1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(+.f64 -1 (neg.f64 (/.f64 1/2 x)))
(-.f64 -1 (/.f64 1/2 x))
(+.f64 -1 (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (/.f64 -1/2 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 -1 (/.f64 1/2 x)) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) -1) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4)))
(fma.f64 x (*.f64 x 1/2) (*.f64 -1/8 (pow.f64 x 4)))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/8 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/2) (*.f64 1/16 (pow.f64 x 6))))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) (*.f64 -5/128 (pow.f64 x 8)))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -5/128 (pow.f64 x 8)))))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -5/128 (pow.f64 x 8) (*.f64 -1/8 (pow.f64 x 4)))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 x (*.f64 x 1/2) (fma.f64 -5/128 (pow.f64 x 8) (*.f64 -1/8 (pow.f64 x 4)))))
x
(-.f64 x 1)
(+.f64 x -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) 1)
(+.f64 (/.f64 1/2 x) (+.f64 x -1))
(+.f64 x (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 x (/.f64 1/2 x)) (+.f64 1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/8 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (+.f64 x (-.f64 -1 (/.f64 1/8 (pow.f64 x 3)))))
(+.f64 (-.f64 x 1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 -1 x) 1)
(fma.f64 -1 x -1)
(fma.f64 x -1 -1)
(-.f64 -1 x)
(-.f64 (*.f64 -1 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (neg.f64 x) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (fma.f64 x -1 -1) (/.f64 -1/2 x))
(+.f64 (-.f64 -1 x) (/.f64 -1/2 x))
(+.f64 -1 (-.f64 (/.f64 -1/2 x) x))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 -1 x) (/.f64 -1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (-.f64 (/.f64 -1/2 x) x)))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/6 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 5) 3/40 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 2) (log.f64 x)))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 -3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -3/32 (pow.f64 x 4)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6))) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6)))) (/.f64 -3/32 (pow.f64 x 4))))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 5/96 (pow.f64 x 6)) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (+.f64 (log.f64 x) (/.f64 -3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 1/2) (+.f64 (log.f64 (/.f64 -1 x)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x)))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (log.f64 (/.f64 -1 x)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x))))
(+.f64 (log.f64 1/2) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (-.f64 (log.f64 (/.f64 -1 x)) (/.f64 5/96 (pow.f64 x 6)))) (/.f64 -1/4 (*.f64 x x)))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (+.f64 (log.f64 1/2) (+.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 -5/96 (pow.f64 x 6)))) (log.f64 (/.f64 -1 x))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -5/96 (pow.f64 x 6))))))

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
✓0.3b
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))
0.5b
(+.f64 x (hypot.f64 1 x))
1.7b
(log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
Compiler

Compiled 58 to 42 computations (27.6% saved)

series6.0ms (0.1%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
1.0ms
x
@inf
(log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
1.0ms
x
@0
(log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
0.0ms
x
@0
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))
0.0ms
x
@inf
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))

rewrite72.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
763×pow1_binary64
707×add-log-exp_binary64
707×log1p-expm1-u_binary64
707×expm1-log1p-u_binary64
690×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
116524
2196724
Stop Event
1×node limit
Counts
2 → 42
Calls
Call 1
Inputs
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))
(log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4)) (log.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (sqrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 2)) (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2)) (log.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) (log.f64 (sqrt.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 2) (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) (sqrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))))))

simplify90.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
728×fma-def_binary64
543×distribute-lft-out_binary64
506×unswap-sqr_binary64
421×*-commutative_binary64
404×distribute-rgt-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043132
1109132
2273132
3795132
43047132
55420132
66288132
77093132
87577132
Stop Event
1×node limit
Counts
50 → 56
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -1/12 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5))))
(+.f64 (*.f64 -5/224 (pow.f64 x 7)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5)))))
(+.f64 (log.f64 1/2) (log.f64 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 11/180 (pow.f64 x 4)) (log.f64 x))))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 11/180 (pow.f64 x 4)) (+.f64 (*.f64 -191/5670 (pow.f64 x 6)) (log.f64 x)))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -1/12 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 -1/12 (pow.f64 x 3)))
(fma.f64 -1/12 (pow.f64 x 3) (*.f64 1/2 x))
(*.f64 x (fma.f64 x (*.f64 x -1/12) 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5))))
(fma.f64 1/2 x (fma.f64 -1/12 (pow.f64 x 3) (*.f64 3/80 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (*.f64 x -1/12) 1/2) (*.f64 3/80 (pow.f64 x 5)))
(+.f64 (*.f64 -5/224 (pow.f64 x 7)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/12 (pow.f64 x 3)) (*.f64 3/80 (pow.f64 x 5)))))
(fma.f64 -5/224 (pow.f64 x 7) (fma.f64 1/2 x (fma.f64 -1/12 (pow.f64 x 3) (*.f64 3/80 (pow.f64 x 5)))))
(fma.f64 x (fma.f64 x (*.f64 x -1/12) 1/2) (fma.f64 3/80 (pow.f64 x 5) (*.f64 -5/224 (pow.f64 x 7))))
(fma.f64 -1/12 (pow.f64 x 3) (fma.f64 -5/224 (pow.f64 x 7) (fma.f64 3/80 (pow.f64 x 5) (*.f64 1/2 x))))
(+.f64 (log.f64 1/2) (log.f64 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (log.f64 x)))
(fma.f64 -1/6 (*.f64 x x) (+.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 x) (fma.f64 -1/6 (*.f64 x x) (log.f64 1/2)))
(+.f64 (log.f64 x) (fma.f64 x (*.f64 x -1/6) (log.f64 1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 11/180 (pow.f64 x 4)) (log.f64 x))))
(fma.f64 -1/6 (*.f64 x x) (+.f64 (log.f64 1/2) (fma.f64 11/180 (pow.f64 x 4) (log.f64 x))))
(+.f64 (fma.f64 11/180 (pow.f64 x 4) (log.f64 x)) (fma.f64 -1/6 (*.f64 x x) (log.f64 1/2)))
(+.f64 (log.f64 1/2) (fma.f64 x (*.f64 x -1/6) (fma.f64 11/180 (pow.f64 x 4) (log.f64 x))))
(+.f64 (log.f64 x) (fma.f64 x (*.f64 x -1/6) (fma.f64 11/180 (pow.f64 x 4) (log.f64 1/2))))
(+.f64 (*.f64 -1/6 (pow.f64 x 2)) (+.f64 (log.f64 1/2) (+.f64 (*.f64 11/180 (pow.f64 x 4)) (+.f64 (*.f64 -191/5670 (pow.f64 x 6)) (log.f64 x)))))
(fma.f64 -1/6 (*.f64 x x) (+.f64 (log.f64 1/2) (fma.f64 11/180 (pow.f64 x 4) (fma.f64 -191/5670 (pow.f64 x 6) (log.f64 x)))))
(+.f64 (fma.f64 11/180 (pow.f64 x 4) (fma.f64 -191/5670 (pow.f64 x 6) (log.f64 x))) (fma.f64 -1/6 (*.f64 x x) (log.f64 1/2)))
(+.f64 (log.f64 1/2) (fma.f64 x (*.f64 x -1/6) (fma.f64 11/180 (pow.f64 x 4) (fma.f64 -191/5670 (pow.f64 x 6) (log.f64 x)))))
(+.f64 (log.f64 x) (fma.f64 x (*.f64 x -1/6) (fma.f64 11/180 (pow.f64 x 4) (fma.f64 -191/5670 (pow.f64 x 6) (log.f64 1/2)))))

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
Compiler

Compiled 20 to 16 computations (20% saved)

series66.0ms (0.8%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
35.0ms
x
@-inf
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
21.0ms
x
@0
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
11.0ms
x
@inf
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))

rewrite61.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
835×pow1_binary64
776×add-log-exp_binary64
776×log1p-expm1-u_binary64
776×expm1-log1p-u_binary64
761×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
089
11696
221096
Stop Event
1×node limit
Counts
1 → 35
Calls
Call 1
Inputs
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 -1) (-.f64 (log.f64 x) (log.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (log.f64 (/.f64 (/.f64 -1 x) 1/2))) (/.f64 (pow.f64 (log.f64 1/2) 2) (log.f64 (/.f64 (/.f64 -1 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (log.f64 1/2) (log.f64 -1)) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 2) (cbrt.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (/.f64 -1/2 x))) (sqrt.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 3) (pow.f64 (log.f64 1/2) 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (*.f64 (log.f64 1/2) (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (pow.f64 (log.f64 1/2) 2)) (/.f64 1 (log.f64 (/.f64 (/.f64 -1 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (*.f64 (log.f64 1/2) (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))))) (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 3) (pow.f64 (log.f64 1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (log.f64 (/.f64 (/.f64 -1 x) 1/2)) (-.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (pow.f64 (log.f64 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 3) (pow.f64 (log.f64 1/2) 3)) (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (*.f64 (log.f64 1/2) (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 3) (pow.f64 (log.f64 1/2) 3)) (+.f64 (pow.f64 (log.f64 1/2) 2) (-.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (*.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (pow.f64 (log.f64 1/2) 2)) (log.f64 (/.f64 (/.f64 -1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 3) (pow.f64 (log.f64 1/2) 3))) (neg.f64 (+.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (*.f64 (log.f64 1/2) (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 (/.f64 -1 x)) 2) (pow.f64 (log.f64 1/2) 2))) (neg.f64 (log.f64 (/.f64 (/.f64 -1 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 1/2) 2) (pow.f64 (log.f64 (/.f64 -1 x)) 2)) (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (/.f64 -1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (/.f64 -1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 -1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (/.f64 -1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 -1/2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (log.f64 (/.f64 -1 x)) (log.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (log.f64 1/2) (log.f64 (/.f64 -1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 -1 x))) 2) (cbrt.f64 (log.f64 (/.f64 -1 x))) (log.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (log.f64 1/2)) 2) (cbrt.f64 (log.f64 1/2)) (log.f64 (/.f64 -1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 (/.f64 -1 x))) (sqrt.f64 (log.f64 (/.f64 -1 x))) (log.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 1/2)) (sqrt.f64 (log.f64 1/2)) (log.f64 (/.f64 -1 x)))))))

simplify29.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
126×fma-neg_binary64
125×fma-def_binary64
55×cancel-sign-sub-inv_binary64
34×distribute-rgt-in_binary64
31×associate--r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
015120
128104
251104
380104
4140104
5262104
6390104
7511104
8625104
9691104
10693104
Stop Event
1×saturated
Counts
43 → 38
Calls
Call 1
Inputs
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
Outputs
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (*.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))
(+.f64 (log.f64 (/.f64 1 x)) (+.f64 (log.f64 -1) (log.f64 1/2)))
(+.f64 (log.f64 -1) (+.f64 (log.f64 1/2) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1) (-.f64 (log.f64 1/2) (log.f64 x)))
(+.f64 (log.f64 1/2) (-.f64 (log.f64 -1) (log.f64 x)))

eval219.0ms (2.7%)

Compiler

Compiled 8553 to 6694 computations (21.7% saved)

prune68.0ms (0.9%)

Pruning

12 alts after pruning (6 fresh and 6 done)

PrunedKeptTotal
New4715476
Fresh011
Picked101
Done369
Total47512487
Error
0b
Counts
487 → 12
Alt Table
Click to see full alt table
StatusErrorProgram
✓15.2b
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
✓32.1b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
✓48.4b
(log.f64 (/.f64 -1/2 x))
✓32.4b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶43.6b
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
✓44.1b
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓46.6b
(log.f64 (*.f64 x 2))
▶27.8b
(log1p.f64 x)
▶62.0b
(log1p.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1)))
▶32.2b
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
▶48.4b
(neg.f64 (log.f64 (/.f64 x -1/2)))
31.1b
x
Compiler

Compiled 150 to 116 computations (22.7% saved)

localize2.0ms (0%)

Compiler

Compiled 4 to 2 computations (50% saved)

localize9.0ms (0.1%)

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 1 x)
✓0.3b
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
✓2.7b
(-.f64 (hypot.f64 1 x) (-.f64 1 x))
Compiler

Compiled 24 to 17 computations (29.2% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
0.0ms
x
@0
(-.f64 (hypot.f64 1 x) (-.f64 1 x))
0.0ms
x
@inf
(-.f64 (hypot.f64 1 x) (-.f64 1 x))
0.0ms
x
@inf
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
0.0ms
x
@-inf
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))

rewrite63.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
879×pow1_binary64
820×expm1-log1p-u_binary64
819×add-log-exp_binary64
819×log1p-expm1-u_binary64
803×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0722
115522
2215122
Stop Event
1×node limit
Counts
2 → 55
Calls
Call 1
Inputs
(-.f64 (hypot.f64 1 x) (-.f64 1 x))
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 x) (neg.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 x) (*.f64 (neg.f64 (-.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) (fma.f64 (neg.f64 (-.f64 1 x)) 1 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 1 x))) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (-.f64 1 x)) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (hypot.f64 1 x) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (hypot.f64 1 x) -1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 2) (cbrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) (sqrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 (-.f64 1 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 x) (+.f64 (hypot.f64 1 x) (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (+.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 x) 2)) (/.f64 1 (+.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (-.f64 1 x))) (-.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 x) (+.f64 (hypot.f64 1 x) (-.f64 1 x)))) (-.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 (-.f64 1 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (hypot.f64 1 x) (-.f64 1 x)) (-.f64 (+.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 (-.f64 1 x) 3)) (+.f64 (+.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 x) (+.f64 (hypot.f64 1 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 x) 2)) (+.f64 (hypot.f64 1 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 (-.f64 1 x) 3))) (neg.f64 (+.f64 (+.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 x) (+.f64 (hypot.f64 1 x) (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (+.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 x) 2))) (neg.f64 (+.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 (neg.f64 (-.f64 1 x)) 3)) (+.f64 (+.f64 1 (*.f64 x x)) (-.f64 (*.f64 (neg.f64 (-.f64 1 x)) (neg.f64 (-.f64 1 x))) (*.f64 (hypot.f64 1 x) (neg.f64 (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3) (pow.f64 x 3)) (+.f64 (*.f64 (+.f64 (hypot.f64 1 x) -1) (+.f64 (hypot.f64 1 x) -1)) (-.f64 (*.f64 x x) (*.f64 (+.f64 (hypot.f64 1 x) -1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 (neg.f64 (-.f64 1 x)) (neg.f64 (-.f64 1 x)))) (-.f64 (hypot.f64 1 x) (neg.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (hypot.f64 1 x) -1) (+.f64 (hypot.f64 1 x) -1)) (*.f64 x x)) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 x) (neg.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 x)) 2) (cbrt.f64 (hypot.f64 1 x)) (neg.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) (neg.f64 (-.f64 1 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) 2) (cbrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) (sqrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (-.f64 (hypot.f64 1 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))))))))

simplify70.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
506×unswap-sqr_binary64
414×associate-/r*_binary64
407×associate-*l*_binary64
318×associate-*r*_binary64
299×associate--l+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
088380
1259365
2721365
32231365
47062365
Stop Event
1×node limit
Counts
79 → 98
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 1)
(fma.f64 2 x -1)
(fma.f64 x 2 -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(+.f64 (/.f64 1/2 x) (fma.f64 2 x -1))
(+.f64 (fma.f64 x 2 -1) (/.f64 1/2 x))
(fma.f64 x 2 (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 2 x -1)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (-.f64 -1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 (+.f64 (/.f64 1/2 x) -1)) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 -1) (+.f64 (/.f64 1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(+.f64 -1 (neg.f64 (/.f64 1/2 x)))
(+.f64 -1 (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (/.f64 -1/2 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (+.f64 -1 (/.f64 -1/16 (pow.f64 x 5)))))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/6 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (/.f64 (/.f64 1/4 x) x) (log.f64 x)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 2) (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (+.f64 (log.f64 2) (/.f64 (/.f64 1/4 x) x)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 (/.f64 -1/4 x) x))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6))) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (/.f64 (/.f64 1/4 x) x) (/.f64 5/96 (pow.f64 x 6))) (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (log.f64 x))) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (-.f64 (log.f64 x) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 (/.f64 -1/4 x) x)))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 (/.f64 1/4 x) x)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 (/.f64 -1/4 x) x))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (/.f64 (/.f64 1/4 x) x) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (+.f64 (log.f64 1/2) (-.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 5/96 (pow.f64 x 6)))) (log.f64 (/.f64 -1 x))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (-.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 5/96 (pow.f64 x 6))))))

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))
✓0.3b
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
✓1.0b
(+.f64 (hypot.f64 1 x) -1)
✓1.0b
(+.f64 x (+.f64 (hypot.f64 1 x) -1))
Compiler

Compiled 46 to 35 computations (23.9% saved)

series4.0ms (0%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 x (+.f64 (hypot.f64 1 x) -1))
0.0ms
x
@-inf
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
0.0ms
x
@inf
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
0.0ms
x
@0
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
0.0ms
x
@-inf
(+.f64 x (+.f64 (hypot.f64 1 x) -1))

rewrite88.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
729×prod-diff_binary64
546×unpow-prod-down_binary64
382×log-prod_binary64
296×fma-def_binary64
251×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
119139
2246139
Stop Event
1×node limit
Counts
4 → 232
Calls
Call 1
Inputs
(+.f64 x (+.f64 (hypot.f64 1 x) -1))
(+.f64 (hypot.f64 1 x) -1)
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
(log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log1p.f64 (pow.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2) (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 (-.f64 x -1) (hypot.f64 1 x))) (/.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (-.f64 (-.f64 x -1) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2))) (log.f64 (-.f64 1 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2)) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (/.f64 1 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (pow.f64 (/.f64 1 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (/.f64 1 (-.f64 (-.f64 x -1) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (pow.f64 (/.f64 1 (-.f64 (-.f64 x -1) (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2) (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 2) 3) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (-.f64 (-.f64 x -1) (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))) (neg.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))) (neg.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (-.f64 1 (*.f64 (+.f64 x (hypot.f64 1 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (*.f64 x x)) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) 1) (-.f64 (+.f64 x (hypot.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 (hypot.f64 1 x) -1)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3))))) 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(2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2)) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (/.f64 1 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (pow.f64 (/.f64 1 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (/.f64 1 (-.f64 (-.f64 x -1) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (pow.f64 (/.f64 1 (-.f64 (-.f64 x -1) (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2) (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 2) 3) (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3)) (+.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (-.f64 (-.f64 x -1) (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))) (neg.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))) (neg.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) (-.f64 1 (*.f64 (+.f64 x (hypot.f64 1 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2) (*.f64 x x)) (-.f64 (+.f64 (hypot.f64 1 x) -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2) 1) (-.f64 (+.f64 x (hypot.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (+.f64 (hypot.f64 1 x) -1) (-.f64 (+.f64 (hypot.f64 1 x) -1) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (-.f64 x -1) (hypot.f64 1 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 (hypot.f64 1 x) -1)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 x) -1))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 x) (+.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (hypot.f64 1 x) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (hypot.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 x) 1 (+.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 x) -1) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (/.f64 1 (+.f64 (hypot.f64 1 x) 1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x x)) (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) 2) (cbrt.f64 (+.f64 (hypot.f64 1 x) -1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (fma.f64 x x 1)) (+.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (hypot.f64 1 x)) (+.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 (hypot.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) (sqrt.f64 (+.f64 (hypot.f64 1 x) -1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) (+.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 -1 (pow.f64 (hypot.f64 1 x) 3)) (/.f64 1 (-.f64 (+.f64 (fma.f64 x x 1) 1) (*.f64 (hypot.f64 1 x) -1))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (hypot.f64 1 x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) 2) (cbrt.f64 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) (sqrt.f64 (+.f64 1 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (hypot.f64 1 x)) 1) (-.f64 (sqrt.f64 (hypot.f64 1 x)) 1) x)))))

simplify58.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
641×associate-*l*_binary64
483×associate-*r*_binary64
415×associate-/r*_binary64
368×fma-def_binary64
338×associate--l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0106662
1316642
2879640
32698640
Stop Event
1×node limit
Counts
280 → 224
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4)))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) (*.f64 -5/128 (pow.f64 x 8)))))
x
(-.f64 x 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(*.f64 -1 x)
(-.f64 (*.f64 -1 x) 1)
(-.f64 (*.f64 -1 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 1)
(fma.f64 2 x -1)
(fma.f64 x 2 -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(+.f64 (/.f64 1/2 x) (fma.f64 2 x -1))
(+.f64 (fma.f64 x 2 -1) (/.f64 1/2 x))
(fma.f64 x 2 (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 2 x -1)) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (fma.f64 x 2 (/.f64 1/2 x)) (+.f64 1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 -1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(+.f64 -1 (neg.f64 (/.f64 1/2 x)))
(-.f64 -1 (/.f64 1/2 x))
(+.f64 -1 (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (/.f64 -1/2 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 -1 (/.f64 1/2 x)) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) -1) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4)))
(fma.f64 x (*.f64 x 1/2) (*.f64 -1/8 (pow.f64 x 4)))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/8 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/2) (*.f64 1/16 (pow.f64 x 6))))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) (*.f64 -5/128 (pow.f64 x 8)))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -5/128 (pow.f64 x 8)))))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -5/128 (pow.f64 x 8) (*.f64 -1/8 (pow.f64 x 4)))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 x (*.f64 x 1/2) (fma.f64 -5/128 (pow.f64 x 8) (*.f64 -1/8 (pow.f64 x 4)))))
x
(-.f64 x 1)
(+.f64 x -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) 1)
(+.f64 (/.f64 1/2 x) (+.f64 x -1))
(+.f64 x (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 x (/.f64 1/2 x)) (+.f64 1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/8 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (+.f64 x (-.f64 -1 (/.f64 1/8 (pow.f64 x 3)))))
(+.f64 (-.f64 x 1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 -1 x) 1)
(fma.f64 -1 x -1)
(fma.f64 x -1 -1)
(-.f64 -1 x)
(-.f64 (*.f64 -1 x) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (neg.f64 x) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (fma.f64 x -1 -1) (/.f64 -1/2 x))
(+.f64 (-.f64 -1 x) (/.f64 -1/2 x))
(+.f64 -1 (-.f64 (/.f64 -1/2 x) x))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 -1 x) (/.f64 -1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (-.f64 (/.f64 -1/2 x) x)))
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/6 x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 x))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 (pow.f64 x 5) 3/40 (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 5) 3/40 (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 -5/112 (pow.f64 x 7) x)))
(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 2) (log.f64 x)))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (log.f64 2) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 -3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -3/32 (pow.f64 x 4)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6))) (/.f64 1/4 (*.f64 x x)))) (/.f64 3/32 (pow.f64 x 4)))
(+.f64 (log.f64 x) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6)))) (/.f64 -3/32 (pow.f64 x 4))))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 5/96 (pow.f64 x 6)) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (+.f64 (log.f64 x) (/.f64 -3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 1/2) (+.f64 (log.f64 (/.f64 -1 x)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x)))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (log.f64 (/.f64 -1 x)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 1/2) (/.f64 (/.f64 -1/4 x) x))))
(+.f64 (log.f64 1/2) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (-.f64 (log.f64 (/.f64 -1 x)) (/.f64 5/96 (pow.f64 x 6)))) (/.f64 -1/4 (*.f64 x x)))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (+.f64 (log.f64 1/2) (+.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 -5/96 (pow.f64 x 6)))) (log.f64 (/.f64 -1 x))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -5/96 (pow.f64 x 6))))))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 1)
(fma.f64 2 x -1)
(fma.f64 x 2 -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(+.f64 (/.f64 1/2 x) (fma.f64 2 x -1))
(+.f64 (fma.f64 x 2 -1) (/.f64 1/2 x))
(fma.f64 x 2 (+.f64 (/.f64 1/2 x) -1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 2 x -1)) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (fma.f64 x 2 (/.f64 1/2 x)) (+.f64 1 (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 -1) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(+.f64 -1 (neg.f64 (/.f64 1/2 x)))
(-.f64 -1 (/.f64 1/2 x))
(+.f64 -1 (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (/.f64 -1/2 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (+.f64 1 (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 -1 (/.f64 1/2 x)) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) -1) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.0b
(-.f64 x (hypot.f64 1 x))
✓1.7b
(+.f64 (-.f64 x (hypot.f64 1 x)) 1)
✓12.8b
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1))
✓20.3b
(-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))
Compiler

Compiled 85 to 59 computations (30.6% saved)

series5.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))
1.0ms
x
@inf
(-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))
0.0ms
x
@-inf
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1))
0.0ms
x
@0
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1))
0.0ms
x
@-inf
(-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))

rewrite120.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
664×log-prod_binary64
618×fma-def_binary64
406×fma-neg_binary64
250×log1p-udef_binary64
249×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01361
130561
2443061
Stop Event
1×node limit
Counts
4 → 323
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1))
(+.f64 (-.f64 x (hypot.f64 1 x)) 1)
(-.f64 x (hypot.f64 1 x))
Outputs
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simplify74.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
542×distribute-lft-out_binary64
518×sub-neg_binary64
450×times-frac_binary64
381×unswap-sqr_binary64
370×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0106579
1319567
2841567
32306567
45100567
Stop Event
1×node limit
Counts
371 → 405
Calls
Call 1
Inputs
(pow.f64 x 2)
(+.f64 (*.f64 -1/4 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 -1/4 (pow.f64 x 4)) (+.f64 (pow.f64 x 2) (*.f64 1/8 (pow.f64 x 6))))
(+.f64 (*.f64 -5/64 (pow.f64 x 8)) (+.f64 (*.f64 -1/4 (pow.f64 x 4)) (+.f64 (pow.f64 x 2) (*.f64 1/8 (pow.f64 x 6)))))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 2)
(-.f64 (+.f64 (*.f64 2 x) (/.f64 1 x)) 2)
(-.f64 (+.f64 (*.f64 2 x) (/.f64 1 x)) (+.f64 2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(*.f64 -2 x)
(-.f64 (*.f64 -2 x) 2)
(-.f64 (*.f64 -2 x) (+.f64 2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 -2 x)) (+.f64 2 (/.f64 1 x)))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(-.f64 (*.f64 2 x) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) x)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(*.f64 2 x)
(+.f64 1 (*.f64 2 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
-1
(-.f64 x 1)
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x) 1)
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) 1)
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/4 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 -1/4 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 -1/4 (pow.f64 x 4)))
(+.f64 (*.f64 -1/4 (pow.f64 x 4)) (+.f64 (pow.f64 x 2) (*.f64 1/8 (pow.f64 x 6))))
(+.f64 (fma.f64 -1/4 (pow.f64 x 4) (*.f64 x x)) (*.f64 1/8 (pow.f64 x 6)))
(fma.f64 -1/4 (pow.f64 x 4) (fma.f64 x x (*.f64 1/8 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 -1/4 (pow.f64 x 4) (*.f64 1/8 (pow.f64 x 6))))
(fma.f64 -1/4 (pow.f64 x 4) (fma.f64 1/8 (pow.f64 x 6) (*.f64 x x)))
(+.f64 (*.f64 -5/64 (pow.f64 x 8)) (+.f64 (*.f64 -1/4 (pow.f64 x 4)) (+.f64 (pow.f64 x 2) (*.f64 1/8 (pow.f64 x 6)))))
(fma.f64 -5/64 (pow.f64 x 8) (+.f64 (fma.f64 -1/4 (pow.f64 x 4) (*.f64 x x)) (*.f64 1/8 (pow.f64 x 6))))
(fma.f64 -5/64 (pow.f64 x 8) (fma.f64 -1/4 (pow.f64 x 4) (fma.f64 x x (*.f64 1/8 (pow.f64 x 6)))))
(fma.f64 -1/4 (pow.f64 x 4) (fma.f64 -5/64 (pow.f64 x 8) (fma.f64 1/8 (pow.f64 x 6) (*.f64 x x))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 2)
(fma.f64 2 x -2)
(fma.f64 x 2 -2)
(-.f64 (+.f64 (*.f64 2 x) (/.f64 1 x)) 2)
(+.f64 (fma.f64 2 x (/.f64 1 x)) -2)
(+.f64 (/.f64 1 x) (fma.f64 x 2 -2))
(+.f64 (fma.f64 x 2 -2) (/.f64 1 x))
(-.f64 (+.f64 (*.f64 2 x) (/.f64 1 x)) (+.f64 2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (fma.f64 2 x (/.f64 1 x)) (+.f64 2 (/.f64 1/4 (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 (/.f64 1 x)) (+.f64 2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 -2 (-.f64 (fma.f64 x 2 (/.f64 1 x)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (fma.f64 x 2 -2) (/.f64 1 x)) (/.f64 -1/4 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 -2) (-.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))))
(*.f64 -2 x)
(*.f64 x -2)
(-.f64 (*.f64 -2 x) 2)
(fma.f64 -2 x -2)
(fma.f64 x -2 -2)
(-.f64 (*.f64 -2 x) (+.f64 2 (/.f64 1 x)))
(-.f64 (fma.f64 -2 x -2) (/.f64 1 x))
(-.f64 (fma.f64 x -2 -2) (/.f64 1 x))
(+.f64 -2 (fma.f64 x -2 (/.f64 -1 x)))
(fma.f64 x -2 (+.f64 -2 (/.f64 -1 x)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 -2 x)) (+.f64 2 (/.f64 1 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (fma.f64 -2 x -2) (/.f64 1 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (fma.f64 x -2 -2) (/.f64 1 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 -2 (fma.f64 x -2 (/.f64 -1 x))))
(-.f64 (fma.f64 x -2 (+.f64 -2 (/.f64 -1 x))) (/.f64 -1/4 (pow.f64 x 3)))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 (*.f64 x x) 1/2 x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) -1/8 x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 6) 1/16 (fma.f64 (pow.f64 x 4) -1/8 x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (pow.f64 x 6) 1/16 x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (*.f64 2 x) 1)
(fma.f64 2 x -1)
(fma.f64 x 2 -1)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) 1)
(+.f64 (/.f64 1/2 x) (fma.f64 2 x -1))
(+.f64 (fma.f64 x 2 -1) (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 2 x -1)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (-.f64 (fma.f64 x 2 -1) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 -1) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (fma.f64 x 2 -1) (+.f64 (/.f64 1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
-1
(neg.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 x))))
(+.f64 -1 (neg.f64 (/.f64 1/2 x)))
(-.f64 -1 (/.f64 1/2 x))
(+.f64 -1 (/.f64 -1/2 x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) 1))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 -1 (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 -1 (/.f64 -1/2 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (+.f64 1 (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (+.f64 1 (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (+.f64 -1 (/.f64 -1/2 x)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (-.f64 -1 (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (+.f64 -1 (/.f64 -1/2 x)) (/.f64 -1/16 (pow.f64 x 5))))
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(fma.f64 -1/2 (*.f64 x x) x)
(fma.f64 (*.f64 x x) -1/2 x)
(fma.f64 x (*.f64 x -1/2) x)
(+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 -1/2 (*.f64 x x) x))
(fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (*.f64 x x) -1/2 x))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/8 x))
(+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) x)))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) x)))
(fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (*.f64 x x) -1/2 (fma.f64 (pow.f64 x 6) -1/16 x)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (pow.f64 x 6) -1/16 x)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1 (/.f64 1/2 x))
(+.f64 1 (/.f64 -1/2 x))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(+.f64 1 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 1 (-.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 1 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (+.f64 1 (/.f64 -1/2 x)) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 1 (+.f64 (-.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 1 (*.f64 2 x))
(+.f64 (*.f64 x 2) 1)
(fma.f64 x 2 1)
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x)))
(+.f64 (/.f64 1/2 x) (+.f64 (*.f64 x 2) 1))
(+.f64 1 (fma.f64 x 2 (/.f64 1/2 x)))
(+.f64 (/.f64 1/2 x) (fma.f64 x 2 1))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1 (*.f64 2 x))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 (*.f64 x 2) 1) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 1 (fma.f64 x 2 (/.f64 1/2 x))) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (+.f64 (fma.f64 x 2 1) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 1 (fma.f64 x 2 (/.f64 -1/8 (pow.f64 x 3)))))
(+.f64 1 (+.f64 (/.f64 1/2 x) (fma.f64 x 2 (/.f64 -1/8 (pow.f64 x 3)))))
-1
(-.f64 x 1)
(+.f64 x -1)
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x) 1)
(+.f64 (fma.f64 -1/2 (*.f64 x x) x) -1)
(+.f64 (fma.f64 (*.f64 x x) -1/2 x) -1)
(+.f64 x (fma.f64 x (*.f64 x -1/2) -1))
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) 1)
(+.f64 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 -1/2 (*.f64 x x) x)) -1)
(+.f64 (fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (*.f64 x x) -1/2 x)) -1)
(+.f64 (fma.f64 x (*.f64 x -1/2) x) (fma.f64 (pow.f64 x 4) 1/8 -1))
(+.f64 (fma.f64 (*.f64 x x) -1/2 x) (fma.f64 (pow.f64 x 4) 1/8 -1))
(+.f64 (fma.f64 (pow.f64 x 4) 1/8 x) (fma.f64 x (*.f64 x -1/2) -1))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (/.f64 -1/16 (pow.f64 x 5)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 5/128 (pow.f64 x 7)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
(+.f64 (-.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (+.f64 (/.f64 5/128 (pow.f64 x 7)) (/.f64 -1/16 (pow.f64 x 5))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 2 x (/.f64 1/2 x))
(fma.f64 x 2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (fma.f64 2 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (fma.f64 x 2 (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (fma.f64 2 x (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (fma.f64 x 2 (/.f64 -1/8 (pow.f64 x 3)))))

eval404.0ms (5.1%)

Compiler

Compiled 17687 to 13476 computations (23.8% saved)

prune137.0ms (1.7%)

Pruning

11 alts after pruning (2 fresh and 9 done)

PrunedKeptTotal
New7631764
Fresh011
Picked101
Done1910
Total76511776
Error
0b
Counts
776 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
✓15.2b
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
✓32.1b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
✓48.4b
(log.f64 (/.f64 -1/2 x))
✓32.4b
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓43.6b
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
✓44.1b
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓46.6b
(log.f64 (*.f64 x 2))
✓27.8b
(log1p.f64 x)
60.6b
(log1p.f64 (/.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 (neg.f64 (-.f64 1 x)) (neg.f64 (-.f64 1 x)))) (-.f64 (hypot.f64 1 x) (neg.f64 (-.f64 1 x)))))
✓48.4b
(neg.f64 (log.f64 (/.f64 x -1/2)))
31.1b
x
Compiler

Compiled 94 to 72 computations (23.4% saved)

regimes58.0ms (0.7%)

Counts
22 → 2
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
(log.f64 (*.f64 x 2))
(log.f64 (/.f64 -1/2 x))
(neg.f64 (log.f64 (/.f64 x -1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x (hypot.f64 1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(log1p.f64 (/.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 (neg.f64 (-.f64 1 x)) (neg.f64 (-.f64 1 x)))) (-.f64 (hypot.f64 1 x) (neg.f64 (-.f64 1 x)))))
(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(log1p.f64 (log1p.f64 (expm1.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1)))))
(log1p.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 (hypot.f64 1 x) -1) 2)) (+.f64 (-.f64 x (hypot.f64 1 x)) 1)))
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (exp.f64 (log.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))
Outputs
(neg.f64 (log.f64 (/.f64 x -1/2)))
(log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1)))
Calls

3 calls:

34.0ms
x
10.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Results
ErrorSegmentsBranch
0.4b2x
8.9b2(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.9b2(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
Compiler

Compiled 213 to 156 computations (26.8% saved)

bsearch25.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
25.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes30.0ms (0.4%)

Counts
12 → 3
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
(log.f64 (*.f64 x 2))
(log.f64 (/.f64 -1/2 x))
(neg.f64 (log.f64 (/.f64 x -1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x (hypot.f64 1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(log1p.f64 (-.f64 (hypot.f64 1 x) (-.f64 1 x)))
Outputs
(neg.f64 (log.f64 (/.f64 x -1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x (hypot.f64 1 x)))
Calls

1 calls:

28.0ms
x
Results
ErrorSegmentsBranch
0.0b3x
Compiler

Compiled 59 to 43 computations (27.1% saved)

bsearch55.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
31.0ms
1.5838595381056368e-6
0.2091445065733028
23.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes23.0ms (0.3%)

Counts
8 → 3
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
(log.f64 (*.f64 x 2))
(log.f64 (/.f64 -1/2 x))
(neg.f64 (log.f64 (/.f64 x -1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
Outputs
(neg.f64 (log.f64 (/.f64 x -1/2)))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (*.f64 x 2))
Calls

1 calls:

21.0ms
x
Results
ErrorSegmentsBranch
0.2b3x
Compiler

Compiled 31 to 21 computations (32.3% saved)

bsearch47.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
22.0ms
0.2091445065733028
43654445621966.81
25.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes16.0ms (0.2%)

Counts
7 → 3
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
(log.f64 (*.f64 x 2))
(log.f64 (/.f64 -1/2 x))
(neg.f64 (log.f64 (/.f64 x -1/2)))
Outputs
(neg.f64 (log.f64 (/.f64 x -1/2)))
x
(log.f64 (*.f64 x 2))
Calls

1 calls:

14.0ms
x
Results
ErrorSegmentsBranch
0.5b3x
Compiler

Compiled 24 to 16 computations (33.3% saved)

bsearch52.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
26.0ms
0.2091445065733028
43654445621966.81
26.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes18.0ms (0.2%)

Counts
6 → 3
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
(log.f64 (*.f64 x 2))
(log.f64 (/.f64 -1/2 x))
Outputs
(log.f64 (/.f64 -1/2 x))
x
(log.f64 (*.f64 x 2))
Calls

1 calls:

17.0ms
x
Results
ErrorSegmentsBranch
0.5b3x
Compiler

Compiled 19 to 12 computations (36.8% saved)

bsearch52.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
24.0ms
0.2091445065733028
43654445621966.81
29.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes11.0ms (0.1%)

Counts
4 → 2
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
(log.f64 (/.f64 -1/2 x))
Outputs
(log.f64 (/.f64 -1/2 x))
(log1p.f64 x)
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
12.5b2x
Compiler

Compiled 11 to 6 computations (45.5% saved)

bsearch23.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
23.0ms
-3017661112.169902
-0.0012643448271952562
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes17.0ms (0.2%)

Counts
3 → 2
Calls
Call 1
Inputs
x
x
(log1p.f64 x)
Outputs
x
(log1p.f64 x)
Calls

1 calls:

16.0ms
x
Results
ErrorSegmentsBranch
26.5b2x
Compiler

Compiled 7 to 3 computations (57.1% saved)

bsearch31.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
31.0ms
0.2091445065733028
43654445621966.81
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts
2 → 1
Calls
Call 1
Inputs
x
x
Outputs
x
Calls

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
31.1b1x
Compiler

Compiled 5 to 2 computations (60% saved)

simplify16.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
5×+-commutative_binary64
3×*-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041179
153179
256179
357179
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 7479565196323457/4722366482869645213696) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 3767612487480451/18014398509481984) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 3767612487480451/18014398509481984) x (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 3767612487480451/18014398509481984) x (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (log.f64 (/.f64 -1/2 x)) (log1p.f64 x))
(if (<=.f64 x 3767612487480451/18014398509481984) x (log1p.f64 x))
x
Outputs
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (log1p.f64 (+.f64 x (-.f64 (hypot.f64 1 x) 1))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (log1p.f64 (+.f64 x (+.f64 (hypot.f64 1 x) -1))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 7479565196323457/4722366482869645213696) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 7479565196323457/4722366482869645213696) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 3767612487480451/18014398509481984) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 3767612487480451/18014398509481984) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (neg.f64 (log.f64 (/.f64 x -1/2))) (if (<=.f64 x 3767612487480451/18014398509481984) x (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 3767612487480451/18014398509481984) x (log.f64 (*.f64 x 2))))
(if (<=.f64 x -3164247018354667/1048576) (log.f64 (/.f64 -1/2 x)) (log1p.f64 x))
(if (<=.f64 x 3767612487480451/18014398509481984) x (log1p.f64 x))
x
Compiler

Compiled 128 to 94 computations (26.6% saved)

soundness36.0ms (0.4%)

Algorithm
3×egg-herbie
Rules
2×+-commutative_binary64
2×+-commutative_binary64
2×+-commutative_binary64
1×1-exp_binary64
1×hypot-1-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0812
1139
2149
0812
1139
2149
0812
1139
2149
Stop Event
1×saturated
1×saturated
1×saturated
Compiler

Compiled 81 to 57 computations (29.6% saved)

end126.0ms (1.6%)

Compiler

Compiled 121 to 86 computations (28.9% saved)

Profiling

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