Details

Time bar (total: 12.9s)

analyze1.1s (8.5%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
6.2%93.7%0.1%5
6.2%90.5%3.2%6
21.9%67.1%11%7
23.4%64.8%11.8%8
32%52.7%15.3%9
33.2%51.3%15.5%10
37.7%45.2%17.2%11
38.3%44.4%17.2%12
40.6%41.3%18%13
41%41%18%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample228.0ms (1.8%)

Algorithm
1×intervals
Results
18.0ms180×body128valid
15.0ms38×body1024valid
7.0ms22×body1024nan
6.0ms24×body512valid
5.0ms24×body512nan
2.0ms11×body256valid
2.0ms13×body256nan
2.0ms3×body2048valid
1.0ms20×body128nan
0.0ms1×body2048nan
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify230.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
2748×fma-def_binary64
1264×fma-neg_binary64
934×associate--r-_binary64
475×cancel-sign-sub-inv_binary64
423×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01018
12217
24017
38615
416315
534415
666615
7121715
8146315
9160815
10178715
11232215
12292615
13298715
14308915
15313315
16314215
17314215
18322515
19323315
20323715
21497915

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
20.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶20.3b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
Compiler

Compiled 48 to 35 computations (27.1% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓2.7b
(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series217.0ms (1.7%)

Counts
2 → 48
Calls

2 calls:

128.0ms
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
89.0ms
(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

rewrite10.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
9×prod-diff_binary64
5×add-log-exp_binary64
Counts
2 → 43
Calls

2 calls:

5.0ms
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
1.0ms
(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify144.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
640×associate-+r+_binary64
380×associate-+l+_binary64
221×associate-/r*_binary64
199×associate--r+_binary64
178×+-commutative_binary64
Counts
91 → 163
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03935598
111525346
250655346

prune317.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1585163
Fresh000
Picked011
Done000
Total1586164
Error
0.1b
Counts
164 → 6
Alt Table
StatusErrorProgram
▶20.4b
(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
34.9b
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
46.5b
(-.f64 1 (+.f64 (+.f64 (/.f64 1/3 (*.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (+.f64 (/.f64 x (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (log1p.f64 (neg.f64 x)) (+.f64 (/.f64 (*.f64 x x) (*.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (/.f64 1 (*.f64 y y))))))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (+.f64 (/.f64 x (*.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (fma.f64 1/2 (/.f64 (*.f64 x x) (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (+.f64 (/.f64 1/2 (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (fma.f64 1/3 (/.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (/.f64 x (*.f64 y (-.f64 1 x))))))))))
40.1b
(-.f64 1 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))))
✓20.3b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
59.9b
(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))
Compiler

Compiled 8242 to 5766 computations (30% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
✓0.1b
(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
✓2.7b
(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))

series1.4s (10.8%)

Counts
3 → 72
Calls

3 calls:

1.2s
(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
165.0ms
(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
17.0ms
(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))

rewrite72.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
24×times-frac_binary64
21×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64
18×log-prod_binary64
Counts
3 → 86
Calls

3 calls:

22.0ms
(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
22.0ms
(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
20.0ms
(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))

simplify494.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
465×+-commutative_binary64
409×associate-+r+_binary64
273×*-commutative_binary64
269×fma-def_binary64
205×associate-/r*_binary64
Counts
158 → 211
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0121016961
1435715633
2499815633
3496915633

prune858.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2101211
Fresh314
Picked101
Done011
Total2143217
Error
0b
Counts
217 → 3
Alt Table
StatusErrorProgram
▶0.0b
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
34.9b
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
✓20.3b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
Compiler

Compiled 20124 to 14663 computations (27.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
✓0.0b
(/.f64 (-.f64 1 x) y)
✓0.2b
(/.f64 (E.f64) (-.f64 1 x))
✓0.8b
(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))

series123.0ms (1%)

Counts
4 → 76
Calls

4 calls:

81.0ms
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
24.0ms
(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
11.0ms
(/.f64 (-.f64 1 x) y)
6.0ms
(/.f64 (E.f64) (-.f64 1 x))

rewrite308.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Rules
195×times-frac_binary64
175×add-sqr-sqrt_binary64
171×*-un-lft-identity_binary64
94×add-cube-cbrt_binary64
46×difference-of-squares_binary64
Counts
4 → 229
Calls

4 calls:

228.0ms
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
16.0ms
(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
10.0ms
(/.f64 (-.f64 1 x) y)
8.0ms
(/.f64 (E.f64) (-.f64 1 x))

simplify327.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
339×times-frac_binary64
300×associate-/l*_binary64
264×associate-/r*_binary64
214×associate-/r/_binary64
200×associate-*l/_binary64
Counts
305 → 378
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05637825
114237444
249017444
349497444

prune533.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New3780378
Fresh011
Picked011
Done011
Total3783381
Error
0b
Counts
381 → 3
Alt Table
StatusErrorProgram
✓0.0b
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
▶34.9b
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
✓20.3b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
Compiler

Compiled 10131 to 6122 computations (39.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
✓0.0b
(log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓1.2b
(exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))))
2.7b
(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series1.1s (8.3%)

Counts
3 → 72
Calls

3 calls:

829.0ms
(log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
139.0ms
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
101.0ms
(exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))))

rewrite26.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
20×log-prod_binary64
18×prod-diff_binary64
Counts
3 → 76
Calls

3 calls:

9.0ms
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
3.0ms
(exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))))
1.0ms
(log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

simplify511.0ms (4%)

Algorithm
1×egg-herbie
Rules
898×fma-def_binary64
416×+-commutative_binary64
360×associate-+r+_binary64
228×*-commutative_binary64
215×associate-/r*_binary64
Counts
148 → 255
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0107915796
1338415092
2496314975
3513914975

prune1.2s (9.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3220322
Fresh000
Picked011
Done022
Total3223325
Error
0b
Counts
325 → 3
Alt Table
StatusErrorProgram
✓0.0b
(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
✓34.9b
(-.f64 1 (exp.f64 (log.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))))
✓20.3b
(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
Compiler

Compiled 25553 to 18765 computations (26.6% saved)

regimes763.0ms (5.9%)

Accuracy

Total 0.0b remaining (55.1%)

Threshold costs 0.0b (55.1%)

Counts
76 → 1
Compiler

Compiled 7250 to 5770 computations (20.4% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01123
11823
22723
33323
43723
53823
63723

end1.0ms (0%)

Compiler

Compiled 16 to 12 computations (25% saved)

sample2.9s (22.2%)

Algorithm
1×intervals
Results
694.0ms5857×body128valid
497.0ms1024×body1024valid
380.0ms1020×body1024nan
233.0ms674×body512valid
177.0ms641×body512nan
79.0ms376×body256valid
60.0ms343×body256nan
43.0ms69×body2048valid
40.0ms484×body128nan
1.0ms2×body2048nan
Compiler

Compiled 75 to 58 computations (22.7% saved)

Profiling

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