Details

Time bar (total: 1.3s)

analyze3.0ms (0.2%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample650.0ms (49%)

Results
640.0ms8256×body256valid
0.0ms2×body256invalid
Bogosity

preprocess127.0ms (9.6%)

Algorithm
2×egg-herbie
Rules
600×unsub-neg_binary64
586×distribute-rgt-out--_binary64
492×fma-neg_binary64
430×distribute-neg-in_binary64
411×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2209
3319
4489
5769
61239
73409
87079
914969
1028539
1142809
1252529
1355629
1458669
1559629
1660409
1763089
1872549
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify114.0ms (8.6%)

Algorithm
1×egg-herbie
Rules
600×unsub-neg_binary64
586×distribute-rgt-out--_binary64
492×fma-neg_binary64
430×distribute-neg-in_binary64
411×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2209
3319
4489
5769
61239
73409
87079
914969
1028539
1142809
1252529
1355629
1458669
1559629
1660409
1763089
1872549
Stop Event
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

Compiled 17 to 8 computations (52.9% saved)

series3.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

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

rewrite42.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
580×pow1_binary64
544×add-log-exp_binary64
543×log1p-expm1-u_binary64
543×expm1-log1p-u_binary64
531×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
112616
2154816
Stop Event
1×node limit
Counts
2 → 55
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (neg.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 1 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (*.f64 x (neg.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x))) (*.f64 x (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x)))) (-.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (*.f64 x (neg.f64 x))))))))

simplify53.0ms (4%)

Algorithm
1×egg-herbie
Rules
505×div-sub_binary64
493×fma-neg_binary64
460×fma-def_binary64
372×cancel-sign-sub-inv_binary64
239×distribute-neg-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01661063
1412945
21429876
34624876
Stop Event
1×node limit
Counts
79 → 122
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(-.f64 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x)))))
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(*.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))
(+.f64 1 (*.f64 x (neg.f64 x)))
(+.f64 1 (*.f64 (*.f64 x (neg.f64 x)) 1))
(+.f64 (*.f64 x (neg.f64 x)) 1)
(*.f64 1 (-.f64 1 (*.f64 x x)))
(*.f64 (-.f64 1 (*.f64 x x)) 1)
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (*.f64 x x))))
(*.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(*.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 1 (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (+.f64 1 (pow.f64 (*.f64 x (neg.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x))) (*.f64 x (neg.f64 x)))))
(/.f64 (-.f64 1 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x)))) (-.f64 1 (*.f64 x (neg.f64 x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 3)
(sqrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))
(log.f64 (exp.f64 (-.f64 1 (*.f64 x x))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (*.f64 x x))))
(log1p.f64 (expm1.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (log1p.f64 (*.f64 x (neg.f64 x))))
Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (*.f64 x x) 1) (*.f64 -1/8 (pow.f64 x 4)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (*.f64 x x) 1) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -1/16 (pow.f64 x 6))))
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(/.f64 (-.f64 1 (pow.f64 x 6)) (fma.f64 x (+.f64 x (pow.f64 x 3)) 1))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (+.f64 1 (*.f64 x x))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (*.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (+.f64 1 (pow.f64 (*.f64 x (neg.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x))) (*.f64 x (neg.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (+.f64 (pow.f64 x 6) -1) (-.f64 -1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (fma.f64 x (+.f64 x (pow.f64 x 3)) 1))
(/.f64 (-.f64 1 (*.f64 (*.f64 x (neg.f64 x)) (*.f64 x (neg.f64 x)))) (-.f64 1 (*.f64 x (neg.f64 x))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (*.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(pow.f64 (-.f64 1 (*.f64 x x)) 1)
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2)
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) 1/2)
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3) 1/3)
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 3)
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(sqrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(log.f64 (exp.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(expm1.f64 (log1p.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(log1p.f64 (expm1.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(exp.f64 (log1p.f64 (*.f64 x (neg.f64 x))))

eval34.0ms (2.5%)

Compiler

Compiled 1699 to 1239 computations (27.1% saved)

prune14.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1202122
Fresh000
Picked011
Done000
Total1203123
Error
0b
Counts
123 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.6b
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1.1b
1
Compiler

Compiled 17 to 13 computations (23.5% saved)

localize6.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite134.0ms (10.1%)

Algorithm
1×batch-egg-rewrite
Rules
432×pow1_binary64
420×add-sqr-sqrt_binary64
411×*-un-lft-identity_binary64
401×add-log-exp_binary64
401×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11027
211487
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 -1/2 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))))))

simplify64.0ms (4.9%)

Algorithm
1×egg-herbie
Rules
1079×log-prod_binary64
420×associate-*l*_binary64
379×associate-*r*_binary64
325×associate-+l+_binary64
306×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
046216
1102206
2359191
33009191
46280191
Stop Event
1×node limit
Counts
26 → 18
Calls
Call 1
Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 -1/2 (*.f64 x x)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(-.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)
(pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)
(pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))
Outputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(+.f64 0 (*.f64 -1/2 (*.f64 x x)))
(*.f64 -1/2 (*.f64 x x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(*.f64 -1/2 (*.f64 x x))
(-.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)
(*.f64 -1/2 (*.f64 x x))
(pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)
(*.f64 -1/2 (*.f64 x x))
(pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)
(*.f64 -1/2 (*.f64 x x))
(pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)
(*.f64 -1/2 (*.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(*.f64 -1/2 (*.f64 x x))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(*.f64 -1/2 (*.f64 x x))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(*.f64 -1/2 (*.f64 x x))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))
(*.f64 -1/2 (*.f64 x x))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))
(exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))

eval4.0ms (0.3%)

Compiler

Compiled 206 to 147 computations (28.6% saved)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New18018
Fresh011
Picked011
Done011
Total18321
Error
0b
Counts
21 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.6b
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1.1b
1
Compiler

Compiled 17 to 13 computations (23.5% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.6b
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1.1b
1
Compiler

Compiled 17 to 13 computations (23.5% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.6b
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1.1b
1
Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes10.0ms (0.7%)

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

4 calls:

3.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms
(-.f64 1 (*.f64 x x))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b1(-.f64 1 (*.f64 x x))
0.0b1(*.f64 x x)
Compiler

Compiled 34 to 22 computations (35.3% saved)

regimes31.0ms (2.4%)

Accuracy

Total -0.6b remaining (-98.2%)

Threshold costs -0.6b (-98.2%)

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

2 calls:

28.0ms
(*.f64 x x)
3.0ms
x
Results
ErrorSegmentsBranch
0.6b1x
0.6b1(*.f64 x x)
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify3.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
11820
22520
32920
43120
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
1
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
(+.f64 1 (*.f64 (*.f64 x x) -1/2))
1
Compiler

Compiled 17 to 13 computations (23.5% saved)

soundness0.0ms (0%)

end20.0ms (1.5%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

Profiling

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