Details

Time bar (total: 3.5s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%0%50%4
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.2s (64.7%)

Results
905.0ms2092×body1024valid
553.0ms4378×body128valid
476.0ms1038×body512valid
168.0ms259×body2048valid
113.0ms489×body256valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0711
1128
2178
3248
4318
5488
6738
7938
81108
91208
101248
111268
121128

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
28.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶28.1b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
Compiler

Compiled 29 to 20 computations (31% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.9b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
✓2.9b
(log.f64 (+.f64 N 1))

series7.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

4.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms
(log.f64 (+.f64 N 1))

rewrite46.0ms (1.3%)

Algorithm
2×batch-egg-rewrite
Rules
745×log1p-expm1-u_binary64
745×expm1-log1p-u_binary64
431×prod-diff_binary64
71×add-sqr-sqrt_binary64
70×egg-rr
Counts
2 → 70
Calls

2 calls:

44.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
44.0ms
(log.f64 (+.f64 N 1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
114811
2182211
3534811
000
100

simplify52.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
577×fma-def_binary64
379×times-frac_binary64
324×fma-neg_binary64
282×associate-+l+_binary64
274×associate--l+_binary64
Counts
94 → 103
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056376
1163350
2443346
31237335
44414335
55036335

prune58.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1003103
Fresh000
Picked101
Done000
Total1013104
Error
0.0b
Counts
104 → 3
Alt Table
StatusErrorProgram
33.8b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
▶28.0b
(log.f64 (/.f64 (+.f64 N 1) N))
28.1b
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
Compiler

Compiled 1415 to 669 computations (52.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (+.f64 N 1) N)
✓1.8b
(log.f64 (/.f64 (+.f64 N 1) N))

series5.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
2.0ms
(/.f64 (+.f64 N 1) N)

rewrite53.0ms (1.5%)

Algorithm
2×batch-egg-rewrite
Rules
635×log1p-expm1-u_binary64
635×expm1-log1p-u_binary64
292×log-prod_binary64
115×fma-def_binary64
108×log1p-udef_binary64
Counts
2 → 104
Calls

2 calls:

51.0ms
(/.f64 (+.f64 N 1) N)
51.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
112615
2159415
3524015
000
100

simplify73.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
736×fma-neg_binary64
510×cancel-sign-sub-inv_binary64
415×times-frac_binary64
285×associate-/l/_binary64
261×div-sub_binary64
Counts
128 → 120
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035255
195253
2227253
3591250
41672250
54252250
64704250
74910250

prune55.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1200120
Fresh022
Picked011
Done000
Total1203123
Error
0.0b
Counts
123 → 3
Alt Table
StatusErrorProgram
33.8b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓28.0b
(log.f64 (/.f64 (+.f64 N 1) N))
▶28.1b
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
Compiler

Compiled 1545 to 872 computations (43.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(pow.f64 (log1p.f64 N) 2)
✓0.3b
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
✓0.5b
(pow.f64 (log.f64 N) 2)
✓1.9b
(-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2))

series73.0ms (2.1%)

Counts
4 → 44
Calls

4 calls:

32.0ms
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
29.0ms
(pow.f64 (log.f64 N) 2)
7.0ms
(-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2))
5.0ms
(pow.f64 (log1p.f64 N) 2)

rewrite100.0ms (2.9%)

Algorithm
2×batch-egg-rewrite
Rules
541×log-prod_binary64
446×fma-def_binary64
288×egg-rr
235×fma-neg_binary64
194×expm1-udef_binary64
Counts
4 → 288
Calls

4 calls:

92.0ms
(pow.f64 (log1p.f64 N) 2)
92.0ms
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
92.0ms
(pow.f64 (log.f64 N) 2)
92.0ms
(-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01050
122734
2292334
3572634
000
100

simplify100.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
502×cancel-sign-sub-inv_binary64
352×sub-neg_binary64
307×fma-neg_binary64
282×associate-+r+_binary64
263×fma-def_binary64
Counts
332 → 358
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02512656
18262609
232802329
349892323
450472323

prune221.0ms (6.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3562358
Fresh011
Picked101
Done011
Total3574361
Error
0.0b
Counts
361 → 4
Alt Table
StatusErrorProgram
▶33.8b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓28.0b
(log.f64 (/.f64 (+.f64 N 1) N))
61.9b
(/.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) 3) 1/3) (+.f64 (log1p.f64 N) (log.f64 N)))
33.9b
(/.f64 (+.f64 (*.f64 2 (/.f64 (log.f64 N) N)) (-.f64 (/.f64 1 (*.f64 N N)) (/.f64 (log.f64 N) (*.f64 N N)))) (+.f64 (log1p.f64 N) (log.f64 N)))
Compiler

Compiled 10739 to 5672 computations (47.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓0.7b
(/.f64 1/2 (*.f64 N N))

series5.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

2.0ms
(/.f64 1/2 (*.f64 N N))
2.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))

rewrite60.0ms (1.7%)

Algorithm
2×batch-egg-rewrite
Rules
924×expm1-log1p-u_binary64
666×prod-diff_binary64
128×egg-rr
89×add-sqr-sqrt_binary64
88×log1p-expm1-u_binary64
Counts
2 → 128
Calls

2 calls:

57.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
57.0ms
(/.f64 1/2 (*.f64 N N))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0820
118417
2234117
3522817
000
100

simplify86.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
732×times-frac_binary64
554×fma-neg_binary64
533×associate-/r*_binary64
495×associate-/l/_binary64
434×unswap-sqr_binary64
Counts
152 → 134
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013216
126216
243216
397216
4222216
5706216
63218216
74900216
84868216
94987216
104913216

prune70.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1331134
Fresh112
Picked101
Done011
Total1353138
Error
0.0b
Counts
138 → 3
Alt Table
StatusErrorProgram
✓28.0b
(log.f64 (/.f64 (+.f64 N 1) N))
61.9b
(/.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) 3) 1/3) (+.f64 (log1p.f64 N) (log.f64 N)))
33.7b
(/.f64 (-.f64 1 (/.f64 1/2 N)) N)
Compiler

Compiled 2714 to 1741 computations (35.9% saved)

regimes64.0ms (1.8%)

Accuracy

Total 0.1b remaining (43.2%)

Threshold costs 0.1b (43.2%)

Counts
28 → 2
Compiler

Compiled 690 to 474 computations (31.3% saved)

bsearch1.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
5×+-commutative_binary64
4×sub-neg_binary64
2×*-commutative_binary64
2×neg-sub0_binary64
2×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01735
12435
23435
33835
44035
53835

end59.0ms (1.7%)

Compiler

Compiled 83 to 61 computations (26.5% saved)

Profiling

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