Details

Time bar (total: 1.9s)

analyze16.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
62.5%12.5%25%4
68.7%6.2%25%5
71.8%3.1%25%6
73.4%1.6%25%7
74.2%0.8%25%8
74.6%0.4%25%9
74.8%0.2%25%10
74.9%0.1%25%11
74.9%0%25%12
74.9%0%25%13
74.9%0%25%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample17.0ms (0.9%)

Algorithm
1×intervals
Results
10.0ms256×body128valid
Compiler

Compiled 20 to 16 computations (20% saved)

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×1-exp_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11112
21012

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series60.0ms (3.1%)

Counts
3 → 12
Calls

3 calls:

44.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms
(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
44×*-un-lft-identity_binary64
30×add-sqr-sqrt_binary64
21×distribute-lft-out_binary64
18×times-frac_binary64
16×add-cube-cbrt_binary64
Counts
3 → 82
Calls

3 calls:

6.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms
(sqrt.f64 (+.f64 x 1))

simplify107.0ms (5.6%)

Algorithm
1×egg-herbie
Rules
733×fma-neg_binary64
333×associate-/r*_binary64
321×associate-/l/_binary64
303×associate-*l/_binary64
284×cancel-sign-sub-inv_binary64
Counts
94 → 108
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01231335
12631239
26341227
318781212
443231211
549871211
648751211

prune75.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1044108
Fresh000
Picked101
Done000
Total1054109
Error
0b
Counts
109 → 4
Alt Table
StatusErrorProgram
41.8b
(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
▶0.2b
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
1.4b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
Compiler

Compiled 1618 to 1245 computations (23.1% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓0.2b
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))

series53.0ms (2.7%)

Counts
2 → 8
Calls

2 calls:

44.0ms
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
8.0ms
(+.f64 (sqrt.f64 (+.f64 x 1)) 1)

rewrite17.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
42×*-un-lft-identity_binary64
25×add-sqr-sqrt_binary64
21×distribute-lft-out_binary64
18×times-frac_binary64
15×add-cube-cbrt_binary64
Counts
2 → 66
Calls

2 calls:

7.0ms
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
7.0ms
(+.f64 (sqrt.f64 (+.f64 x 1)) 1)

simplify76.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
737×fma-def_binary64
578×distribute-rgt-in_binary64
530×distribute-lft-in_binary64
456×fma-neg_binary64
237×cancel-sign-sub-inv_binary64
Counts
74 → 105
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0971120
12121031
24881023
313091008
448331008
549701008

prune80.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh033
Picked011
Done000
Total1344138
Error
0b
Counts
138 → 4
Alt Table
StatusErrorProgram
41.8b
(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓0.2b
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
1.4b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
▶0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
Compiler

Compiled 2054 to 1582 computations (23% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
✓0.2b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

series62.0ms (3.2%)

Counts
2 → 8
Calls

2 calls:

48.0ms
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
14.0ms
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

rewrite31.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
156×*-un-lft-identity_binary64
156×times-frac_binary64
108×add-sqr-sqrt_binary64
76×add-cube-cbrt_binary64
64×distribute-lft-out_binary64
Counts
2 → 157
Calls

2 calls:

9.0ms
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
6.0ms
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

simplify159.0ms (8.3%)

Algorithm
1×egg-herbie
Rules
918×fma-neg_binary64
842×fma-def_binary64
286×times-frac_binary64
250×*-commutative_binary64
241×distribute-rgt-in_binary64
Counts
165 → 178
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01343593
12903208
27503139
320883123
442403123
549793123
649183123

prune139.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2360236
Fresh022
Picked011
Done011
Total2364240
Error
0b
Counts
240 → 4
Alt Table
StatusErrorProgram
41.8b
(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓0.2b
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
▶1.4b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
Compiler

Compiled 4459 to 3525 computations (20.9% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
✓1.4b
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))

series195.0ms (10.1%)

Counts
2 → 8
Calls

2 calls:

162.0ms
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
32.0ms
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))

rewrite8.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
9×times-frac_binary64
4×add-cbrt-cube_binary64
Counts
2 → 43
Calls

2 calls:

3.0ms
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
1.0ms
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))

simplify85.0ms (4.4%)

Algorithm
1×egg-herbie
Rules
436×fma-def_binary64
365×distribute-rgt-neg-in_binary64
319×times-frac_binary64
306×associate-/l*_binary64
275×div-sub_binary64
Counts
51 → 63
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
088952
1174869
2380861
3965846
43399846
54527846
64969846

prune52.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New92092
Fresh011
Picked011
Done022
Total92496
Error
0b
Counts
96 → 4
Alt Table
StatusErrorProgram
41.8b
(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓0.2b
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓1.4b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
Compiler

Compiled 1307 to 1000 computations (23.5% saved)

regimes84.0ms (4.4%)

Accuracy

Total 0.2b remaining (96%)

Threshold costs 0.2b (96%)

Counts
36 → 1
Compiler

Compiled 1081 to 843 computations (22% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11212
21012

end0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample554.0ms (28.9%)

Algorithm
1×intervals
Results
317.0ms7996×body128valid
1.0ms4×body2048valid
Compiler

Compiled 58 to 47 computations (19% saved)

Profiling

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