Details

Time bar (total: 3.6s)

analyze0.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
100%25%0%75%0%0%0%1
Compiler

Compiled 6 to 4 computations (33.3% saved)

sample1.1s (32.1%)

Results
1.1s8256×body256valid
Bogosity

preprocess3.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(acosh.f64 x)
Outputs
(acosh.f64 x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify130.0ms (3.6%)

Algorithm
egg-herbie
Rules
1814×rational.json-simplify-35
1350×rational.json-simplify-53
1016×rational.json-simplify-39
864×rational.json-simplify-59
750×rational.json-simplify-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11427
21927
33727
418527
5195727
6590427
7784327
Stop Event
node limit
Counts
1 → 2
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))

eval1.0ms (0%)

Compiler

Compiled 19 to 12 computations (36.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
33.0b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
33.0b
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
Compiler

Compiled 10 to 7 computations (30% saved)

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
30.7b
(sqrt.f64 (-.f64 (*.f64 x x) 1))
Compiler

Compiled 34 to 17 computations (50% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite73.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
1658×bool.json-1
1658×bool.json-2
1630×rational.json-1
1630×rational.json-2
1270×bool.json-3
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
18717
226417
357417
4175117
5553617
Stop Event
node limit
Counts
1 → 14
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x and (sqrt.f64 (+.f64 (*.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x or (sqrt.f64 (+.f64 (*.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))

simplify853.0ms (23.8%)

Algorithm
egg-herbie
Rules
1528×rational.json-simplify-19
1060×rational.json-simplify-59
1008×rational.json-simplify-1
950×rational.json-simplify-2
648×rational.json-simplify-41
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
077728
1152720
2275720
3554720
41215720
53849720
65919720
77123720
87951720
Stop Event
node limit
Counts
26 → 41
Calls
Call 1
Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x))))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(*.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))
(*.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 1/2)
(*.f64 1/2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(/.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4) 4)
(/.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) 8)
(/.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4))) 16)
Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (+.f64 (sqrt.f64 -1) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x))))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 -1 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (neg.f64 x))))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 1/2)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 1/2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2))
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 2) 2)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4) 4)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(/.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) 8)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
(/.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4)) (*.f64 2 (*.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 4))) 16)
(sqrt.f64 (+.f64 -1 (*.f64 x x)))

eval15.0ms (0.4%)

Compiler

Compiled 739 to 579 computations (21.7% saved)

prune6.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New39241
Fresh000
Picked011
Done000
Total39342
Error
0b
Counts
42 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
0.1b
(log.f64 (+.f64 x (-.f64 x (*.f64 1/2 (/.f64 1 x)))))
33.0b
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.3b
(log.f64 (+.f64 x x))
Compiler

Compiled 26 to 18 computations (30.8% saved)

localize4.0ms (0.1%)

Compiler

Compiled 9 to 3 computations (66.7% saved)

localize15.0ms (0.4%)

Compiler

Compiled 38 to 27 computations (28.9% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
0.1b
(log.f64 (+.f64 x (-.f64 x (*.f64 1/2 (/.f64 1 x)))))
33.0b
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.3b
(log.f64 (+.f64 x x))
Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes76.0ms (2.1%)

Accuracy

Total -33.2b remaining (-36467.5%)

Threshold costs -33.2b (-36467.5%)

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

3 calls:

68.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
3.0ms
x
3.0ms
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
Results
ErrorSegmentsBranch
0.1b1x
0.1b1(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.1b1(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
Compiler

Compiled 45 to 30 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01340
Stop Event
done
saturated
Calls
Call 1
Inputs
(log.f64 (+.f64 x (-.f64 x (*.f64 1/2 (/.f64 1 x)))))
(log.f64 (+.f64 x x))
Outputs
(log.f64 (+.f64 x (-.f64 x (*.f64 1/2 (/.f64 1 x)))))
(log.f64 (+.f64 x x))
Compiler

Compiled 16 to 11 computations (31.3% saved)

soundness0.0ms (0%)

end1.2s (34.6%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

Profiling

Loading profile data...