Details

Time bar (total: 5.3s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.6s (48.3%)

Results
1.2s2078×body2048valid
697.0ms4598×body256valid
464.0ms1078×body1024valid
141.0ms502×body512valid
Bogosity

preprocess17.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
8×sub-neg_binary64
8×fma-def_binary64
5×+-commutative_binary64
3×*-commutative_binary64
3×associate-+l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify11.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
8×sub-neg_binary64
8×fma-def_binary64
5×+-commutative_binary64
3×*-commutative_binary64
3×associate-+l-_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

eval1.0ms (0%)

Compiler

Compiled 23 to 21 computations (8.7% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.2b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶13.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 11 to 10 computations (9.1% saved)

localize17.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓2.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 37 to 31 computations (16.2% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite71.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
595×unpow-prod-down_binary64
406×log-prod_binary64
387×prod-diff_binary64
249×pow2_binary64
228×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
120115
2260215
Stop Event
1×node limit
Counts
1 → 55
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (pow.f64 (/.f64 1 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) 3) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (neg.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 -1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)) (-.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 1)))))

simplify75.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
828×cancel-sign-sub-inv_binary64
813×associate-/r*_binary64
717×associate-*r*_binary64
271×sub-neg_binary64
223×associate-+l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
063306
1179272
2553268
31817268
47008268
Stop Event
1×node limit
Counts
67 → 76
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 1/8 (*.f64 x x) (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -1843/32768 (pow.f64 x 8) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 -1843/32768 (pow.f64 x 8)))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 -1843/32768 (pow.f64 x 8)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 1 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (-.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (+.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 -1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))))
(+.f64 1 (-.f64 (+.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) (sqrt.f64 1/2)) (-.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) (sqrt.f64 1/2)) (sqrt.f64 1/2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) (sqrt.f64 1/2)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))

eval72.0ms (1.4%)

Compiler

Compiled 1505 to 1353 computations (10.1% saved)

prune10.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New73376
Fresh000
Picked011
Done000
Total73477
Error
0b
Counts
77 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓13.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶29.2b
(-.f64 1 (sqrt.f64 1/2))
▶33.8b
(*.f64 1/8 (*.f64 x x))
▶12.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 41 to 36 computations (12.2% saved)

localize4.0ms (0.1%)

Compiler

Compiled 11 to 5 computations (54.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.0b
(-.f64 1 (sqrt.f64 1/2))
Compiler

Compiled 9 to 9 computations (0% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite44.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
443×pow1_binary64
438×add-sqr-sqrt_binary64
426×*-un-lft-identity_binary64
418×add-log-exp_binary64
418×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11046
211246
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 1/2 3/2)) (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (-.f64 1 (pow.f64 1/2 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 1/2 3/2))) (neg.f64 (+.f64 3/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 1/2)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 1/2))) (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 1/2)))) (-.f64 1 (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
28 → 28
Calls
Call 1
Inputs
Outputs

localize62.0ms (1.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓0.0b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓1.7b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
Compiler

Compiled 62 to 53 computations (14.5% saved)

series7.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@-inf
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@inf
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.0ms
x
@0
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms
x
@0
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite168.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
614×prod-diff_binary64
581×log-prod_binary64
325×fma-def_binary64
228×log-div_binary64
219×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01152
125440
2366240
Stop Event
1×node limit
Counts
3 → 253
Calls
Call 1
Inputs
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1/2 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))) (cbrt.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))) (/.f64 1 (+.f64 1/4 (+.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (-.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (+.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))))) (#(struct:change #<rule 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simplify67.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
825×fma-def_binary64
650×times-frac_binary64
605×associate-*l*_binary64
450×associate-*r*_binary64
320×associate-/l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01961612
16391385
223221294
Stop Event
1×node limit
Counts
289 → 316
Calls
Call 1
Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)) (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3))))))) (+.f64 (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (+.f64 (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
Outputs
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 (pow.f64 x 4) -3/16 (*.f64 1/4 (*.f64 x x)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 1/4 (*.f64 x x))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -35/256 (pow.f64 x 8) (*.f64 (pow.f64 x 4) -3/16))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (fma.f64 1/4 (*.f64 x x) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/2 x))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 x) (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5)))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 -1/4 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (+.f64 1/2 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3)))))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/8)
(*.f64 x (*.f64 x 1/8))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 (pow.f64 x 4) -11/128))
(fma.f64 (*.f64 x x) 1/8 (*.f64 (pow.f64 x 4) -11/128))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (pow.f64 x 4) -11/128)))
(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (*.f64 x x) 1/8)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -1843/32768 (pow.f64 x 8) (*.f64 (pow.f64 x 4) -11/128))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (pow.f64 x 8) -1843/32768))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (neg.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) x)))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (neg.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) x))) (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (sqrt.f64 1/2))))))
(+.f64 (-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x)) (-.f64 (/.f64 1/64 (*.f64 (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2)))) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2))))) (*.f64 (/.f64 -1/4 (+.f64 1/2 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x)) (-.f64 (/.f64 1/64 (*.f64 x (*.f64 (fma.f64 x (sqrt.f64 1/2) x) (fma.f64 1/2 (sqrt.f64 1/2) 1/4)))) (/.f64 (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x x))))
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(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (fma.f64 x (sqrt.f64 1/2) x)) (/.f64 (-.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/64 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/256 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (fma.f64 1/2 (sqrt.f64 1/2) 1/4))) (*.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (-.f64 (/.f64 (/.f64 1/64 (fma.f64 1/2 (sqrt.f64 1/2) 1/4)) (+.f64 1/2 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (*.f64 1/2 (sqrt.f64 1/2))))) (/.f64 -3/16 (+.f64 1/2 (sqrt.f64 1/2)))))) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/64 (*.f64 x (*.f64 (fma.f64 x (sqrt.f64 1/2) x) (fma.f64 1/2 (sqrt.f64 1/2) 1/4)))))) (-.f64 (/.f64 1/2 (fma.f64 x (sqrt.f64 1/2) x)) (/.f64 (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x x))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(fma.f64 -1/8 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) -1/8 2)
(fma.f64 x (*.f64 x -1/8) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/8 (*.f64 x x) 2) (*.f64 (pow.f64 x 4) 11/128))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 2))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (+.f64 2 (*.f64 (pow.f64 x 4) 11/128))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 2)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (pow.f64 x 6) -69/1024 2)))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (-.f64 (/.f64 -3/32 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (/.f64 -3/32 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2)))) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 1 (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(-.f64 (+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 1 (*.f64 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))) -1/2)) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 1 (/.f64 (/.f64 3/32 (pow.f64 x 3)) (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 3/32 (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))))

eval564.0ms (10.6%)

Compiler

Compiled 18324 to 16480 computations (10.1% saved)

prune46.0ms (0.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New3422344
Fresh000
Picked011
Done033
Total3426348
Error
0b
Counts
348 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
▶28.6b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓33.8b
(*.f64 1/8 (*.f64 x x))
✓13.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓29.2b
(-.f64 1 (sqrt.f64 1/2))
▶28.7b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
✓12.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 65 to 58 computations (10.8% saved)

localize8.0ms (0.2%)

Compiler

Compiled 15 to 15 computations (0% saved)

localize54.0ms (1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓0.0b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 62 to 52 computations (16.1% saved)

series4.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@inf
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@0
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite75.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
649×log-prod_binary64
551×prod-diff_binary64
350×fma-def_binary64
256×expm1-udef_binary64
256×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01324
130024
2415024
Stop Event
1×node limit
Counts
1 → 38
Calls
Call 1
Inputs
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (sqrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/2 (neg.f64 (/.f64 -1/2 x))) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/2 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 2)) 1) (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 2)) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 2)) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) 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(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1/2 (/.f64 -1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))))

simplify46.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
839×times-frac_binary64
513×associate-*l*_binary64
435×fma-def_binary64
415×associate-/l*_binary64
371×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01141101
1412904
21671856
Stop Event
1×node limit
Counts
50 → 59
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(-.f64 1/4 (*.f64 1/4 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 -1/64 x) 1/4) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 -1/64 x) (+.f64 1/4 (*.f64 1/64 (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 x)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 -1/32 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3))))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x))))))) (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
Outputs
(/.f64 -1/4 x)
(-.f64 1/4 (*.f64 1/4 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/4 x))
(+.f64 1/4 (/.f64 -1/4 x))
(-.f64 (+.f64 (*.f64 -1/64 x) 1/4) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (fma.f64 -1/64 x 1/4) (/.f64 1/4 x))
(+.f64 (fma.f64 x -1/64 1/4) (/.f64 -1/4 x))
(+.f64 1/4 (fma.f64 x -1/64 (/.f64 -1/4 x)))
(-.f64 (+.f64 (*.f64 -1/64 x) (+.f64 1/4 (*.f64 1/64 (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 x)))
(-.f64 (+.f64 (fma.f64 -1/64 x 1/4) (*.f64 1/64 (*.f64 x x))) (/.f64 1/4 x))
(+.f64 (fma.f64 x -1/64 (fma.f64 1/64 (*.f64 x x) 1/4)) (/.f64 -1/4 x))
(+.f64 (fma.f64 x -1/64 1/4) (fma.f64 x (*.f64 x 1/64) (/.f64 -1/4 x)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (neg.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) x)))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))) (-.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (neg.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) x))) (*.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))))
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(+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 1/64 (*.f64 (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2))) (fma.f64 1/2 (sqrt.f64 1/2) 1/4))) (+.f64 (/.f64 (+.f64 (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2)))) x) (+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 1/256 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/64 (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 1/2 (sqrt.f64 1/2) 1/4)) (/.f64 1/256 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 1/2 (sqrt.f64 1/2) 1/4)))) (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (pow.f64 x 3))) (/.f64 (+.f64 (/.f64 1/256 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/64 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/4) (pow.f64 x 3))))))) (*.f64 (/.f64 1/4 (+.f64 1/2 (sqrt.f64 1/2))) (-.f64 (/.f64 -3/16 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 x x)))))

eval106.0ms (2%)

Compiler

Compiled 4587 to 4159 computations (9.3% saved)

prune44.0ms (0.8%)

Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New1293132
Fresh000
Picked011
Done055
Total1299138
Error
0b
Counts
138 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
▶55.3b
(+.f64 1/4 (/.f64 -1/4 x))
✓29.2b
(-.f64 1 (sqrt.f64 1/2))
✓28.6b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓33.8b
(*.f64 1/8 (*.f64 x x))
✓13.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶62.0b
(/.f64 -1/4 x)
✓28.7b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
▶29.1b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
✓12.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 86 to 76 computations (11.6% saved)

localize6.0ms (0.1%)

Compiler

Compiled 12 to 9 computations (25% saved)

localize6.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize14.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiled 29 to 25 computations (13.8% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
1.0ms
x
@inf
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
1.0ms
x
@-inf
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))

rewrite62.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
456×log-prod_binary64
369×exp-prod_binary64
270×pow2_binary64
252×pow-prod-down_binary64
185×pow1/3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
122415
2288115
Stop Event
1×node limit
Counts
1 → 52
Calls
Call 1
Inputs
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 -1/2 x)) (*.f64 2 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) (*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 2 (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 2)) (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 2 (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))) (sqrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/2 (neg.f64 (/.f64 -1/2 x))) (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (-.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 1/2))) -2) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (cbrt.f64 (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 1/2))) 2)) (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 1/2))) 2)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (cbrt.f64 (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 1/2)) -1/2) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (hypot.f64 1 (pow.f64 1/2 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) (hypot.f64 1 (pow.f64 1/2 1/4))) (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (hypot.f64 1 (pow.f64 1/2 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (pow.f64 1/2 3/2))) (-.f64 3/2 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 -1/2 x))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 -1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 -1/2 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))) 2)) (cbrt.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2))))) (sqrt.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 -1 (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 -1/2 x))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 1/2)) (log.f64 (+.f64 1/2 (/.f64 -1/2 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (log1p.f64 (sqrt.f64 1/2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1) (log1p.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 (log1p.f64 (sqrt.f64 1/2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1) (*.f64 (log1p.f64 (sqrt.f64 1/2)) 1)))))))

simplify78.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1277×fma-def_binary64
1026×fma-neg_binary64
572×div-sub_binary64
494×distribute-rgt-in_binary64
476×distribute-lft-in_binary64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
015237
134237
267217
3124217
4236190
5472190
6995163
71948163
83414163
94607163
107667163
Stop Event
1×node limit
Counts
64 → 58
Calls
Call 1
Inputs
(/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
Outputs
(/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))
(/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 -1/2 (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 -1/2 (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/2 (fma.f64 (sqrt.f64 1/2) x x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (-.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (+.f64 -1/2 (/.f64 1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))
(/.f64 (-.f64 -1/2 (/.f64 -1/2 x)) (-.f64 -1 (sqrt.f64 1/2)))

eval25.0ms (0.5%)

Compiler

Compiled 916 to 845 computations (7.8% saved)

prune12.0ms (0.2%)

Pruning

10 alts after pruning (1 fresh and 9 done)

PrunedKeptTotal
New57158
Fresh000
Picked011
Done088
Total571067
Error
0b
Counts
67 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
29.6b
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))
✓13.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓55.3b
(+.f64 1/4 (/.f64 -1/4 x))
✓29.2b
(-.f64 1 (sqrt.f64 1/2))
✓28.6b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓33.8b
(*.f64 1/8 (*.f64 x x))
✓62.0b
(/.f64 -1/4 x)
✓28.7b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
✓29.1b
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
✓12.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 99 to 88 computations (11.1% saved)

regimes159.0ms (3%)

Counts
11 → 2
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
(*.f64 1/8 (*.f64 x x))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

22.0ms
x
20.0ms
(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
11.0ms
(/.f64 1 (hypot.f64 1 x))
11.0ms
(/.f64 1 (hypot.f64 1 x))
7.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.0b3x
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(hypot.f64 1 x)
0.0b2(hypot.f64 1 x)
Compiler

Compiled 208 to 183 computations (12% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
38.95802919848851
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes95.0ms (1.8%)

Counts
10 → 2
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
(*.f64 1/8 (*.f64 x x))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

17.0ms
x
11.0ms
(/.f64 1 (hypot.f64 1 x))
10.0ms
(/.f64 1 (hypot.f64 1 x))
10.0ms
(hypot.f64 1 x)
7.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Results
ErrorSegmentsBranch
0.1b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 190 to 167 computations (12.1% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
38.95802919848851
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes92.0ms (1.7%)

Counts
9 → 3
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Calls

13 calls:

17.0ms
x
10.0ms
(/.f64 1 (hypot.f64 1 x))
9.0ms
(/.f64 1 (hypot.f64 1 x))
9.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
6.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.3b3x
0.5b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.5b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.5b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.5b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.5b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.5b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.5b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.5b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.5b2(/.f64 1 (hypot.f64 1 x))
0.5b2(/.f64 1 (hypot.f64 1 x))
0.5b2(hypot.f64 1 x)
0.5b2(hypot.f64 1 x)
Compiler

Compiled 174 to 153 computations (12.1% saved)

bsearch50.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
24.0ms
2.0568407606825256e-16
38.945192758930894
25.0ms
-3608213680744282000.0
-2.65227621469471e-10
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes19.0ms (0.4%)

Counts
7 → 3
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2) (-.f64 1 (sqrt.f64 1/2)))
Outputs
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))
Calls

1 calls:

17.0ms
x
Results
ErrorSegmentsBranch
0.6b3x
Compiler

Compiled 48 to 41 computations (14.6% saved)

bsearch48.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
2.0568407606825256e-16
38.945192758930894
25.0ms
-3608213680744282000.0
-2.65227621469471e-10
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes17.0ms (0.3%)

Counts
5 → 3
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
Outputs
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
Calls

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
0.6b3x
Compiler

Compiled 26 to 21 computations (19.2% saved)

bsearch50.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
25.0ms
2.0568407606825256e-16
38.945192758930894
25.0ms
-3608213680744282000.0
-2.65227621469471e-10
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes13.0ms (0.2%)

Counts
4 → 3
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
Outputs
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
1.2b3x
Compiler

Compiled 20 to 15 computations (25% saved)

bsearch48.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
2.0568407606825256e-16
38.945192758930894
25.0ms
-3608213680744282000.0
-2.65227621469471e-10
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes11.0ms (0.2%)

Counts
3 → 3
Calls
Call 1
Inputs
(/.f64 -1/4 x)
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
Outputs
(+.f64 1/4 (/.f64 -1/4 x))
(*.f64 1/8 (*.f64 x x))
(+.f64 1/4 (/.f64 -1/4 x))
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
26.9b3x
Compiler

Compiled 16 to 11 computations (31.3% saved)

bsearch48.0ms (0.9%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
2.0568407606825256e-16
38.945192758930894
25.0ms
-3608213680744282000.0
-2.65227621469471e-10
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes4.0ms (0.1%)

Accuracy

Total -6.7b remaining (-12.1%)

Threshold costs -6.7b (-12.1%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
55.3b1x
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify15.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
11×+-commutative_binary64
6×sub-neg_binary64
4×*-commutative_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048281
162281
274281
380281
483281
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 1/8 (*.f64 x x)) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 1/8 (*.f64 x x)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -3608213680744282112) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -3608213680744282112) (+.f64 1/4 (/.f64 -1/4 x)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/4 x))))
(+.f64 1/4 (/.f64 -1/4 x))
(/.f64 -1/4 x)
Outputs
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 1/8 (*.f64 x x)) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 1/8 (*.f64 x x)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 (+.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -3608213680744282112) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -3608213680744282112) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -3608213680744282112) (+.f64 1/4 (/.f64 -1/4 x)) (if (<=.f64 x 8343537359529893/40564819207303340847894502572032) (*.f64 1/8 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/4 x))))
(+.f64 1/4 (/.f64 -1/4 x))
(/.f64 -1/4 x)
Compiler

Compiled 200 to 164 computations (18% saved)

soundness112.0ms (2.1%)

Algorithm
3×egg-herbie
Rules
828×cancel-sign-sub-inv_binary64
813×associate-/r*_binary64
717×associate-*r*_binary64
271×sub-neg_binary64
223×associate-+l+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
063306
1179272
2553268
31817268
47008268
01018
12215
22915
33715
44415
55415
66515
77715
88015
Stop Event
1×saturated
1×node limit
1×saturated
Compiler

Compiled 146 to 133 computations (8.9% saved)

end168.0ms (3.2%)

Compiler

Compiled 192 to 150 computations (21.9% saved)

Profiling

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