Details

Time bar (total: 1.1s)

analyze4.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample859.0ms (78.6%)

Results
848.0ms8256×body128valid

preprocess45.0ms (4.1%)

Algorithm
2×egg-herbie
Rules
492×fma-neg_binary64
454×unsub-neg_binary64
411×distribute-rgt-in_binary64
370×fma-def_binary64
363×distribute-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2209
3319
4489
5769
61239
73189
86579
914219
1027459
1141279
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 7 to 5 computations (28.6% saved)

simplify39.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
492×fma-neg_binary64
454×unsub-neg_binary64
411×distribute-rgt-in_binary64
370×fma-def_binary64
363×distribute-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2209
3319
4489
5769
61239
73189
86579
914219
1027459
1141279
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)))

prune2.0ms (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
StatusErrorProgram
▶0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

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

rewrite36.0ms (3.3%)

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
069
11269
215439
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (-.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 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 expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))))

simplify25.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
689×associate-*l*_binary64
643×fma-def_binary64
224×associate-/l/_binary64
213×associate-*r/_binary64
203×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051276
1151256
2450244
31605242
Stop Event
1×node limit
Counts
34 → 45
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)))))
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))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 -1/16 (pow.f64 x 6) 1)))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))
(fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(-.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 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x)) (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/8 (sqrt.f64 -1)) (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 -1))))
(-.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 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (-.f64 (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x)) (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 -1))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(-.f64 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (neg.f64 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x)))
(-.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (*.f64 x (sqrt.f64 -1)))
(-.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 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x))))
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.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)))))
(-.f64 (+.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (neg.f64 (*.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (-.f64 (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(+.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))

prune32.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New44145
Fresh000
Picked011
Done000
Total44246
Error
0b
Counts
46 → 2
Alt Table
StatusErrorProgram
▶0.3b
(fma.f64 -1/2 (*.f64 x x) 1)
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 629 to 483 computations (23.2% saved)

localize3.0ms (0.3%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Error
0b
Counts
2 → 2
Alt Table
StatusErrorProgram
✓0.3b
(fma.f64 -1/2 (*.f64 x x) 1)
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes13.0ms (1.2%)

Accuracy

Total -0.3b remaining (-4143%)

Threshold costs -0.3b (-4143%)

Counts
4 → 1
Compiler

Compiled 40 to 27 computations (32.5% saved)

simplify2.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2209
3249
4269
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

end27.0ms (2.5%)

Stop Event
1×done
Compiler

Compiled 26 to 16 computations (38.5% saved)

Profiling

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