Details

Time bar (total: 7.7s)

analyze1.8s (23.2%)

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)

sample161.0ms (2.1%)

Algorithm
1×intervals
Results
61.0ms256×body128valid
45.0ms117×body2048nan
23.0ms62×body1024nan
8.0ms35×body512nan
3.0ms17×body256nan
1.0ms10×body128nan
Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify176.0ms (2.3%)

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
29.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶29.1b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓0.0b
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓27.1b
(sqrt.f64 (fma.f64 x x -1))

rewrite17.0ms (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:

6.0ms
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
6.0ms
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
2.0ms
(sqrt.f64 (fma.f64 x x -1))

series42.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

18.0ms
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
13.0ms
(sqrt.f64 (fma.f64 x x -1))
10.0ms
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

simplify156.0ms (2%)

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 → 128
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01591395
14011305
210521265
334241265
447731265
549151265

prune125.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1262128
Fresh000
Picked101
Done000
Total1272129
Error
0b
Counts
129 → 2
Alt Table
StatusErrorProgram
29.1b
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
▶0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
Compiler

Compiled 1871 to 1397 computations (25.3% saved)

localize10.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify16.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune3.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done000
Total022
Error
0b
Counts
2 → 2
Alt Table
StatusErrorProgram
▶29.1b
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓0.0b
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓5.7b
(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))
27.1b
(sqrt.f64 (fma.f64 x x -1))

rewrite6.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
3×log-prod_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×add-cube-cbrt_binary64
3×add-exp-log_binary64
Counts
2 → 25
Calls

2 calls:

1.0ms
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
1.0ms
(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))

series69.0ms (0.9%)

Counts
2 → 24
Calls

2 calls:

42.0ms
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
26.0ms
(expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))

simplify347.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
544×fma-def_binary64
286×distribute-rgt-in_binary64
260×fma-neg_binary64
247×cancel-sign-sub-inv_binary64
244×distribute-lft-in_binary64
Counts
49 → 89
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01901703
15331353
22042941
34742940
44995940
54903940

prune398.0ms (5.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh000
Picked011
Done011
Total1722174
Error
0b
Counts
174 → 2
Alt Table
StatusErrorProgram
✓29.1b
(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓0.5b
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
Compiler

Compiled 3318 to 2683 computations (19.1% saved)

regimes88.0ms (1.1%)

Accuracy

Total 0.3b remaining (75.6%)

Threshold costs 0.3b (75.6%)

Compiler

Compiled 414 to 304 computations (26.6% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1710

end1.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

sample4.2s (55.2%)

Algorithm
1×intervals
Results
1.7s4082×body2048nan
849.0ms8000×body128valid
617.0ms1901×body1024nan
257.0ms989×body512nan
75.0ms483×body256nan
41.0ms442×body128nan
3.0ms6×body4096nan
Compiler

Compiled 39 to 29 computations (25.6% saved)

Profiling

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