Details

Time bar (total: 2.3s)

analyze6.0ms (0.3%)

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)

sample1.0s (42.7%)

Results
975.0ms8256×body256valid
1.0ms11×body256invalid

preprocess36.0ms (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)

simplify13.0ms (0.6%)

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)

prune2.0ms (0.1%)

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)

localize21.0ms (0.9%)

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)

series5.0ms (0.2%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
2.0ms
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))

rewrite67.0ms (2.9%)

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)))))))))

simplify81.0ms (3.4%)

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)))

eval12.0ms (0.5%)

Compiler

Compiled 254 to 206 computations (18.9% saved)

prune11.0ms (0.5%)

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
▶31.0b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶0.8b
(-.f64 x 1/2)
2.1b
x
▶0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶0.5b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 33 to 24 computations (27.3% saved)

localize17.0ms (0.7%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓28.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

series2.0ms (0.1%)

Counts
1 → 8
Calls

3 calls:

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

rewrite253.0ms (10.8%)

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)))))))))

simplify72.0ms (3.1%)

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))))

localize18.0ms (0.8%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

localize56.0ms (2.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.0b
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
Compiler

Compiled 40 to 30 computations (25% saved)

series6.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
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)
1.0ms
x
@0
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
1.0ms
x
@-inf
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

rewrite143.0ms (6.1%)

Algorithm
1×batch-egg-rewrite
Rules
824×prod-diff_binary64
521×log-prod_binary64
394×fma-def_binary64
217×expm1-udef_binary64
217×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
124226
2350326
Stop Event
1×node limit
Counts
2 → 108
Calls
Call 1
Inputs
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
Outputs
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x) 3)) (/.f64 1 (fma.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) (-.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 1/4)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1/4 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2)) (/.f64 1 (-.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x -1/2) 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 x -1/2)) (cbrt.f64 (+.f64 x -1/2))) (cbrt.f64 (+.f64 x -1/2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x -1/2)) (sqrt.f64 (+.f64 x -1/2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (+.f64 x -1/2))))))

simplify101.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
758×fma-neg_binary64
496×cancel-sign-sub-inv_binary64
484×associate-/l*_binary64
457×unswap-sqr_binary64
411×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024277
159255
2150255
3356255
4887255
52555255
66344255
Stop Event
1×node limit
Counts
132 → 122
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))))
(/.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 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 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
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)))))
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)))))
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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 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 x) (-.f64 1/8 (/.f64 -1/16 x)))
(/.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 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2)
(-.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 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (-.f64 (/.f64 -1/8 x) 1/2))
(-.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 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (-.f64 (/.f64 -1/8 x) 1/2))
(-.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 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))

localize7.0ms (0.3%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval104.0ms (4.4%)

Compiler

Compiled 2578 to 1955 computations (24.2% saved)

prune70.0ms (3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1581159
Fresh101
Picked011
Done033
Total1595164
Error
0b
Counts
164 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓31.0b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.8b
(-.f64 x 1/2)
2.1b
x
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.5b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 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
✓31.0b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.8b
(-.f64 x 1/2)
2.1b
x
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.5b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 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
✓31.0b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.8b
(-.f64 x 1/2)
2.1b
x
✓0.3b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.5b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 33 to 24 computations (27.3% saved)

regimes26.0ms (1.1%)

Counts
7 → 1
Calls
Call 1
Inputs
x
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:

12.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
10.0ms
x
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 47 to 32 computations (31.9% saved)

regimes10.0ms (0.4%)

Counts
4 → 1
Calls
Call 1
Inputs
x
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
0.5b1x
Compiler

Compiled 15 to 9 computations (40% saved)

regimes11.0ms (0.4%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
0.8b1x
Compiler

Compiled 8 to 4 computations (50% saved)

regimes8.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
2 → 1
Calls
Call 1
Inputs
x
x
Outputs
x
Calls

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
2.1b1x
Compiler

Compiled 5 to 2 computations (60% saved)

simplify6.0ms (0.3%)

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)

soundness134.0ms (5.7%)

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)

end37.0ms (1.6%)

Compiler

Compiled 23 to 16 computations (30.4% saved)

Profiling

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