Details

Time bar (total: 2.2s)

analyze14.0ms (0.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%50%0%0%50%0%2
0%0%50%0%0%50%0%3
33.3%12.5%25%0%0%62.5%0%4
60%18.7%12.5%0%0%68.7%0%5
77.8%21.9%6.2%0%0%71.8%0%6
88.2%23.4%3.1%0%0%73.4%0%7
93.9%24.2%1.6%0%0%74.2%0%8
96.9%24.6%0.8%0%0%74.6%0%9
98.4%24.8%0.4%0%0%74.8%0%10
99.2%24.9%0.2%0%0%74.9%0%11
99.6%24.9%0.1%0%0%74.9%0%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.1s (49.4%)

Results
1.0s8256×body256valid
1.0ms7×body256invalid
Bogosity

preprocess31.0ms (1.5%)

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)

simplify11.0ms (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%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
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)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0.1%)

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))

rewrite47.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
648×pow1_binary64
603×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
587×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11469
217599
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 log1p.f64 (expm1.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)))))))))

simplify61.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
744×associate-/r/_binary64
666×div-sub_binary64
253×*-commutative_binary64
240×fma-def_binary64
234×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03268
18868
224468
367764
4312062
5718662
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 (+.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 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.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 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -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 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.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 (0.3%)

Compiler

Compiled 254 to 206 computations (18.9% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New20525
Fresh000
Picked101
Done000
Total21526
Error
0b
Counts
26 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶32.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶0.1b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶0.2b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
▶0.5b
(-.f64 x 1/2)
1.3b
x
Compiler

Compiled 33 to 24 computations (27.3% saved)

localize10.0ms (0.5%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0.1%)

Counts
1 → 8
Calls

3 calls:

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

rewrite129.0ms (6%)

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
069
11299
216459
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (*.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 log1p.f64 (expm1.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)))))))))

simplify175.0ms (8.1%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
536×fma-neg_binary64
520×div-sub_binary64
498×associate-/r*_binary64
479×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02574
16570
215070
336570
488370
5229270
6768870
Stop Event
1×node limit
Counts
30 → 37
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)))))
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 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 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (-.f64 x 1/2) (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x -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 -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 1/2 x) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))

localize8.0ms (0.4%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

localize16.0ms (0.7%)

Local error

Found 1 expressions with local error:

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

Compiled 40 to 30 computations (25% saved)

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

rewrite99.0ms (4.6%)

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
2218010
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 log1p.f64 (expm1.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)))))))

simplify61.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
505×distribute-neg-frac_binary64
485×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
4425132
51467132
64000132
77470132
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))
(/.f64 (/.f64 -1/16 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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.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 (/.f64 1/16 x) x))
(+.f64 (/.f64 (/.f64 -1/16 x) x) (/.f64 -1/8 x))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval22.0ms (1%)

Compiler

Compiled 918 to 697 computations (24.1% saved)

prune16.0ms (0.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New73073
Fresh011
Picked011
Done033
Total73578
Error
0b
Counts
78 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓32.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.1b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.2b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
✓0.5b
(-.f64 x 1/2)
1.3b
x
Compiler

Compiled 33 to 24 computations (27.3% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune48.0ms (2.2%)

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
✓32.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.1b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.2b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
✓0.5b
(-.f64 x 1/2)
1.3b
x
Compiler

Compiled 33 to 24 computations (27.3% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.2%)

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
✓32.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.1b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.2b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
✓0.5b
(-.f64 x 1/2)
1.3b
x
Compiler

Compiled 33 to 24 computations (27.3% saved)

regimes42.0ms (1.9%)

Counts
6 → 1
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.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:

28.0ms
x
11.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.1b1x
0.1b1(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes9.0ms (0.4%)

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

1 calls:

8.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes8.0ms (0.4%)

Accuracy

Total -0.8b remaining (-155%)

Threshold costs -0.8b (-155%)

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

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
0.5b1x
Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify8.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01531
12231
22331
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 x (+.f64 -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 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x 1/2)
(+.f64 x -1/2)
x
Compiler

Compiled 26 to 19 computations (26.9% saved)

soundness179.0ms (8.3%)

Algorithm
1×egg-herbie
Rules
744×associate-/r/_binary64
666×div-sub_binary64
253×*-commutative_binary64
240×fma-def_binary64
234×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03268
18868
224468
367764
4312062
5718662
Stop Event
1×node limit
Compiler

Compiled 660 to 564 computations (14.5% saved)

end65.0ms (3%)

Compiler

Compiled 23 to 16 computations (30.4% saved)

Profiling

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