Details

Time bar (total: 5.1s)

analyze359.0ms (7%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%50%25%4
25%37.5%37.5%5
25%31.2%43.8%6
25%28.1%46.9%7
25%26.5%48.5%8
25%25.8%49.2%9
25%25.4%49.6%10
25%25.2%49.8%11
25%25.1%49.9%12
25%25%50%13
25%25%50%14
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample233.0ms (4.5%)

Algorithm
1×intervals
Results
24.0ms120×body2048nan
16.0ms256×body128valid
10.0ms62×body1024nan
3.0ms27×body512nan
1.0ms16×body256nan
1.0ms19×body128nan
Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify155.0ms (3%)

Algorithm
1×egg-herbie
Rules
871×fma-neg_binary64
804×unsub-neg_binary64
461×distribute-neg-in_binary64
434×sub-neg_binary64
338×distribute-rgt-out_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11812
22212
33712
46412
511312
624712
750012
8156012
9251312
10321812
11360212
12380312
13397412
14407512
15439212
16483612
17489812
18490112

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
30.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶30.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓28.0b
(sqrt.f64 (fma.f64 x x -1))

series10.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

6.0ms
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms
(sqrt.f64 (fma.f64 x x -1))

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
6×*-un-lft-identity_binary64
5×add-sqr-sqrt_binary64
4×log-prod_binary64
4×add-cube-cbrt_binary64
4×pow1_binary64
Counts
2 → 32
Calls

2 calls:

3.0ms
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms
(sqrt.f64 (fma.f64 x x -1))

simplify71.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
549×fma-neg_binary64
294×associate-/l/_binary64
291×sub-neg_binary64
254×distribute-neg-frac_binary64
221×fma-def_binary64
Counts
56 → 79
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0136988
1330928
2885889
33023888
44940888
54940888

prune46.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New77279
Fresh000
Picked011
Done000
Total77380
Error
0b
Counts
80 → 3
Alt Table
StatusErrorProgram
✓30.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶0.2b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
0.4b
(log.f64 (+.f64 x x))
Compiler

Compiled 1330 to 999 computations (24.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
✓0.2b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
✓0.5b
(/.f64 3/32 (pow.f64 x 4))
✓0.8b
(/.f64 1/4 (*.f64 x x))

series22.0ms (0.4%)

Counts
4 → 36
Calls

4 calls:

8.0ms
(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
6.0ms
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
5.0ms
(/.f64 3/32 (pow.f64 x 4))
3.0ms
(/.f64 1/4 (*.f64 x x))

rewrite124.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Rules
302×add-sqr-sqrt_binary64
296×*-un-lft-identity_binary64
248×times-frac_binary64
240×associate-+r+_binary64
231×prod-diff_binary64
Counts
4 → 400
Calls

4 calls:

37.0ms
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
6.0ms
(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
3.0ms
(/.f64 1/4 (*.f64 x x))
3.0ms
(/.f64 3/32 (pow.f64 x 4))

simplify307.0ms (6%)

Algorithm
1×egg-herbie
Rules
862×times-frac_binary64
716×fma-neg_binary64
197×+-commutative_binary64
188×associate-*r/_binary64
165×associate-+l+_binary64
Counts
436 → 520
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056712318
112439999
227919633
348749633
449789633

prune571.0ms (11.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New5200520
Fresh011
Picked011
Done011
Total5203523
Error
0b
Counts
523 → 3
Alt Table
StatusErrorProgram
✓30.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓0.2b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
▶0.4b
(log.f64 (+.f64 x x))
Compiler

Compiled 22084 to 15909 computations (28% saved)

localize3.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
StatusErrorProgram
✓30.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓0.2b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
✓0.4b
(log.f64 (+.f64 x x))
Compiler

Compiled 32 to 23 computations (28.1% saved)

regimes33.0ms (0.6%)

Accuracy

Total 0.3b remaining (99.5%)

Threshold costs 0.3b (99.5%)

Counts
7 → 1
Compiler

Compiled 291 to 220 computations (24.4% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
5×+-commutative_binary64
4×sub-neg_binary64
2×*-commutative_binary64
2×distribute-neg-frac_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01526
12026
23426
33826
44026
53826

end1.0ms (0%)

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample3.2s (61.8%)

Algorithm
1×intervals
Results
1.8s4081×body2048nan
441.0ms8000×body128valid
323.0ms1972×body1024nan
128.0ms1004×body512nan
40.0ms479×body256nan
21.0ms489×body128nan
3.0ms10×body4096nan
Compiler

Compiled 62 to 46 computations (25.8% saved)

Profiling

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