Details

Time bar (total: 1.0s)

analyze4.0ms (0.4%)

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
25%0%75%13
25%0%75%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample776.0ms (74%)

Results
764.0ms8256×body128valid
0.0ms5×body128invalid

preprocess17.0ms (1.6%)

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 8 to 6 computations (25% saved)

simplify6.0ms (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 (0.1%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

prune2.0ms (0.2%)

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 16 to 12 computations (25% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.3%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
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))

rewrite41.0ms (3.9%)

Algorithm
1×batch-egg-rewrite
Rules
695×pow1_binary64
645×add-log-exp_binary64
645×log1p-expm1-u_binary64
645×expm1-log1p-u_binary64
72×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11469
217719
Stop Event
1×node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (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 log.f64 (+.f64 1 (expm1.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify20.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
527×fma-neg_binary64
470×fma-def_binary64
384×cancel-sign-sub-inv_binary64
346×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01834
14534
210234
325634
464134
5184234
Stop Event
1×node limit
Counts
19 → 22
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)))))
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 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 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 1/8 x) (/.f64 (/.f64 1/16 x) x)))
(-.f64 (+.f64 (+.f64 x -1/2) (/.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 (+.f64 -1/2 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))))

eval5.0ms (0.5%)

Compiler

Compiled 184 to 140 computations (23.9% saved)

prune10.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New20222
Fresh000
Picked101
Done000
Total21223
Error
0b
Counts
23 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶0.4b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize5.0ms (0.5%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done000
Total022
Error
0b
Counts
2 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.4b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 22 to 16 computations (27.3% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓28.3b
(sqrt.f64 (*.f64 x (+.f64 x -1)))

series1.0ms (0.1%)

Counts
1 → 8
Calls

3 calls:

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

rewrite37.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
646×pow1_binary64
602×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
64×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11299
216409
Stop Event
1×node limit
Counts
1 → 23
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (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 log.f64 (+.f64 1 (expm1.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify34.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
539×fma-neg_binary64
468×cancel-sign-sub-inv_binary64
441×fma-def_binary64
347×associate-/l/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02574
16570
215070
336570
488070
5228770
Stop Event
1×node limit
Counts
31 → 38
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 (+.f64 x -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 -1/2 (+.f64 x (/.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 (/.f64 1/16 x) x))))
(+.f64 (-.f64 (+.f64 x -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 -1/2 (/.f64 -1/8 x)) (-.f64 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 (/.f64 1/8 x) (-.f64 1/2 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 (+.f64 (/.f64 1/8 x) (-.f64 1/2 x)) (/.f64 (/.f64 1/16 x) x))
(+.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) (-.f64 1/2 x)))
(+.f64 (+.f64 1/2 (/.f64 1/8 x)) (-.f64 (/.f64 1/16 (*.f64 x x)) x))
(+.f64 (-.f64 1/2 (/.f64 -1/8 x)) (-.f64 (/.f64 1/16 (*.f64 x x)) x))

eval9.0ms (0.8%)

Compiler

Compiled 345 to 258 computations (25.2% saved)

prune41.0ms (3.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New38038
Fresh000
Picked011
Done011
Total38240
Error
0b
Counts
40 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.4b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes10.0ms (1%)

Accuracy

Total -30.7b remaining (-7000.6%)

Threshold costs -30.7b (-7000.6%)

Counts
4 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(*.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 -1/8 x)))
Results
TimeErrorSegmentsBranch
4.0ms0.4b1x
4.0ms0.4b1(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify2.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1910
Stop Event
1×saturated
Calls
Call 1
Inputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Outputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

end15.0ms (1.4%)

Stop Event
1×done
Compiler

Compiled 16 to 12 computations (25% saved)

Profiling

Loading profile data...