Details

Time bar (total: 5.1s)

analyze352.0ms (6.9%)

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)

sample226.0ms (4.4%)

Algorithm
1×intervals
Results
23.0ms123×body2048nan
13.0ms256×body128valid
9.0ms58×body1024nan
4.0ms34×body512nan
1.0ms18×body256nan
0.0ms9×body128nan
Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify158.0ms (3.1%)

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
31.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶31.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓0.0b
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓29.0b
(sqrt.f64 (fma.f64 x x -1))

series14.0ms (0.3%)

Counts
3 → 36
Calls

3 calls:

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

rewrite9.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
7×add-sqr-sqrt_binary64
6×add-cube-cbrt_binary64
5×add-log-exp_binary64
5×pow1_binary64
Counts
3 → 49
Calls

3 calls:

4.0ms
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
3.0ms
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
1.0ms
(sqrt.f64 (fma.f64 x x -1))

simplify81.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
583×fma-neg_binary64
330×sub-neg_binary64
301×fma-def_binary64
254×distribute-neg-frac_binary64
210×associate-+l+_binary64
Counts
85 → 118
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01591395
14011305
210521265
334241265
447731265
549151265

prune529.0ms (10.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1162118
Fresh000
Picked011
Done000
Total1163119
Error
0b
Counts
119 → 3
Alt Table
StatusErrorProgram
✓31.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
▶0.5b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
Compiler

Compiled 1926 to 1439 computations (25.3% saved)

localize467.0ms (9.1%)

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))))
✓0.3b
(/.f64 3/32 (pow.f64 x 4))
✓0.5b
(/.f64 1/4 (*.f64 x x))

series23.0ms (0.4%)

Counts
4 → 36
Calls

4 calls:

11.0ms
(-.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))))
3.0ms
(/.f64 3/32 (pow.f64 x 4))
3.0ms
(/.f64 1/4 (*.f64 x x))

rewrite173.0ms (3.4%)

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:

94.0ms
(+.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))

simplify342.0ms (6.7%)

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

prune560.0ms (10.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New5200520
Fresh011
Picked011
Done011
Total5203523
Error
0b
Counts
523 → 3
Alt Table
StatusErrorProgram
✓31.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓0.5b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
Compiler

Compiled 22090 to 15915 computations (28% saved)

localize5.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
StatusErrorProgram
✓31.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓0.5b
(+.f64 (log.f64 2) (-.f64 (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))) (/.f64 3/32 (pow.f64 x 4))))
Compiler

Compiled 35 to 26 computations (25.7% saved)

regimes42.0ms (0.8%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Counts
14 → 1
Compiler

Compiled 507 to 376 computations (25.8% 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)

sample2.1s (41.5%)

Algorithm
1×intervals
Results
798.0ms4020×body2048nan
420.0ms8000×body128valid
298.0ms1942×body1024nan
115.0ms1033×body512nan
42.0ms553×body256nan
19.0ms479×body128nan
2.0ms10×body4096nan
Compiler

Compiled 65 to 49 computations (24.6% saved)

Profiling

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