Details

Time bar (total: 1.7s)

analyze4.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%50%50%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample830.0ms (49.6%)

Results
815.0ms8256×body256valid
1.0ms12×body256invalid

preprocess15.0ms (0.9%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify9.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))

eval1.0ms (0%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.5b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.5b
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
✓0.5b
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))

series3.0ms (0.2%)

Counts
1 → 8
Calls

3 calls:

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

rewrite40.0ms (2.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11469
217719
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x -1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify46.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
752×associate-/r/_binary64
677×div-sub_binary64
250×*-commutative_binary64
240×fma-def_binary64
237×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03268
18868
224368
366864
4311562
5712062
Stop Event
1×node limit
Counts
22 → 25
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 x -1/2)
(-.f64 x 1/2)
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

eval6.0ms (0.4%)

Compiler

Compiled 254 to 206 computations (18.9% saved)

prune5.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New20525
Fresh000
Picked011
Done000
Total20626
Error
0b
Counts
26 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
▶31.0b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶0.6b
(-.f64 x 1/2)
▶0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶0.4b
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
✓0.5b
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
1.6b
x
Compiler

Compiled 41 to 30 computations (26.8% saved)

localize4.0ms (0.2%)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
✓0.0b
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
1.0ms
x
@-inf
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
0.0ms
x
@inf
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)

rewrite46.0ms (2.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
116310
2217910
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (*.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (neg.f64 (/.f64 -1/16 x))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 -1/8 (/.f64 -1/16 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 -1/8 (/.f64 -1/16 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))

simplify48.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
513×distribute-neg-frac_binary64
490×associate-/l*_binary64
485×fma-neg_binary64
434×unswap-sqr_binary64
360×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017150
137132
277132
3164132
4420132
51446132
63951132
77381132
Stop Event
1×node limit
Counts
43 → 36
Calls
Call 1
Inputs
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
Outputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))

localize7.0ms (0.4%)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
28.9b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
0.0b
(*.f64 x (+.f64 x -1))
✓0.0b
(*.f64 x (+.f64 x -1))
✓28.9b
(sqrt.f64 (*.f64 x (+.f64 x -1)))

series3.0ms (0.2%)

Counts
2 → 20
Calls

6 calls:

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

rewrite55.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
646×pow1_binary64
602×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
590×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
112916
2164016
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.f64 x (+.f64 x -1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (neg.f64 x) 3)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 x x) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 x x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1 (pow.f64 x 3)) x) (fma.f64 x x (-.f64 1 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -1) x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 -1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 x x -1)) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 x -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (neg.f64 x))))))

simplify40.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
673×fma-neg_binary64
616×times-frac_binary64
557×cancel-sign-sub-inv_binary64
501×associate-/r*_binary64
347×associate-/l/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026157
168144
2161144
3394144
4981144
52766144
Stop Event
1×node limit
Counts
66 → 65
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x))))
(+.f64 x (-.f64 (-.f64 -1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (+.f64 x (/.f64 (/.f64 -1/16 x) x)))
(+.f64 -1/2 (-.f64 x (-.f64 (/.f64 (/.f64 1/16 x) x) (/.f64 -1/8 x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(-.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(+.f64 (/.f64 1/8 x) (-.f64 1/2 (+.f64 x (/.f64 (/.f64 -1/16 x) x))))
(+.f64 (/.f64 1/8 x) (+.f64 1/2 (-.f64 (/.f64 (/.f64 1/16 x) x) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)

eval49.0ms (2.9%)

Compiler

Compiled 1206 to 872 computations (27.7% saved)

prune91.0ms (5.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New992101
Fresh101
Picked101
Done134
Total1025107
Error
0b
Counts
107 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶31.0b
(sqrt.f64 (-.f64 (*.f64 x x) x))
1.6b
x
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.4b
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
✓0.6b
(-.f64 x 1/2)
Compiler

Compiled 33 to 23 computations (30.3% saved)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
28.9b
(sqrt.f64 (-.f64 (*.f64 x x) x))
0.0b
(-.f64 (*.f64 x x) x)
✓0.0b
(-.f64 (*.f64 x x) x)
✓28.9b
(sqrt.f64 (-.f64 (*.f64 x x) x))

series2.0ms (0.1%)

Counts
2 → 20
Calls

6 calls:

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

rewrite43.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
572×pow1_binary64
538×add-log-exp_binary64
538×log1p-expm1-u_binary64
538×expm1-log1p-u_binary64
524×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0516
111116
2153616
Stop Event
1×node limit
Counts
2 → 63
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 (*.f64 x x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) (cbrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) (pow.f64 (-.f64 (*.f64 x x) x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 x x))) (sqrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3))) (sqrt.f64 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (-.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2) (cbrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) (*.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (/.f64 1 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (pow.f64 (-.f64 (*.f64 x x) x) 1/4)) (pow.f64 (-.f64 (*.f64 x x) x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 x)) (-.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (cbrt.f64 (-.f64 (*.f64 x x) x))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x))) (-.f64 (pow.f64 x 6) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x 4) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 x x))) (neg.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 x x) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 x x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (neg.f64 x))))))

simplify160.0ms (9.6%)

Algorithm
1×egg-herbie
Rules
673×fma-neg_binary64
616×times-frac_binary64
557×cancel-sign-sub-inv_binary64
501×associate-/r*_binary64
347×associate-/l/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026157
168144
2161144
3394144
4981144
52766144
Stop Event
1×node limit
Counts
83 → 82
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x))))
(+.f64 x (-.f64 (-.f64 -1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (+.f64 x (/.f64 (/.f64 -1/16 x) x)))
(+.f64 -1/2 (-.f64 x (-.f64 (/.f64 (/.f64 1/16 x) x) (/.f64 -1/8 x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(-.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(+.f64 (/.f64 1/8 x) (-.f64 1/2 (+.f64 x (/.f64 (/.f64 -1/16 x) x))))
(+.f64 (/.f64 1/8 x) (+.f64 1/2 (-.f64 (/.f64 (/.f64 1/16 x) x) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)

eval15.0ms (0.9%)

Compiler

Compiled 915 to 389 computations (57.5% saved)

prune19.0ms (1.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New81182
Fresh101
Picked011
Done033
Total82587
Error
0b
Counts
87 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
1.6b
x
✓0.4b
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓31.0b
(sqrt.f64 (-.f64 (*.f64 x x) x))
✓0.6b
(-.f64 x 1/2)
Compiler

Compiled 33 to 23 computations (30.3% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done044
Total055
Error
0b
Counts
5 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
1.6b
x
✓0.4b
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓31.0b
(sqrt.f64 (-.f64 (*.f64 x x) x))
✓0.6b
(-.f64 x 1/2)
Compiler

Compiled 33 to 23 computations (30.3% saved)

regimes33.0ms (2%)

Counts
10 → 1
Calls
Call 1
Inputs
x
x
x
(-.f64 x 1/2)
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(sqrt.f64 (-.f64 (*.f64 x x) x))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
Calls

2 calls:

24.0ms
x
7.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 61 to 39 computations (36.1% saved)

regimes6.0ms (0.3%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
0.4b1x
Compiler

Compiled 16 to 9 computations (43.8% saved)

regimes5.0ms (0.3%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
0.6b1x
Compiler

Compiled 9 to 4 computations (55.6% saved)

regimes5.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts
3 → 1
Calls
Call 1
Inputs
x
x
x
Outputs
x
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
1.6b1x
Compiler

Compiled 6 to 2 computations (66.7% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×+-commutative_binary64
3×sub-neg_binary64
1×*-commutative_binary64
1×distribute-neg-frac_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
12331
23031
33231
43331
Stop Event
1×saturated
Calls
Call 1
Inputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x 1/2)
x
Outputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 x 1/2)
(+.f64 x -1/2)
x

end54.0ms (3.3%)

Stop Event
1×fuel
Compiler

Compiled 49 to 35 computations (28.6% saved)

Profiling

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