Details

Time bar (total: 2.2s)

analyze3.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
62.5%12.5%25%4
68.7%6.2%25%5
71.8%3.1%25%6
73.4%1.6%25%7
74.2%0.8%25%8
74.6%0.4%25%9
74.8%0.2%25%10
74.9%0.1%25%11
74.9%0%25%12
74.9%0%25%13
74.9%0%25%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample774.0ms (35.2%)

Results
746.0ms8252×body128valid
1.0ms4×body2048valid
Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify9.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×1-exp_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11112
21012

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series51.0ms (2.3%)

Counts
2 → 8
Calls

2 calls:

41.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms
(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite53.0ms (2.4%)

Algorithm
2×batch-egg-rewrite
Rules
804×log1p-expm1-u_binary64
804×expm1-log1p-u_binary64
424×prod-diff_binary64
76×add-sqr-sqrt_binary64
72×add-log-exp_binary64
Counts
2 → 67
Calls

2 calls:

52.0ms
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
52.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721
115621
2201521
3566621
000
100

simplify85.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
446×distribute-rgt-out--_binary64
433×fma-def_binary64
394×distribute-rgt-out_binary64
363×distribute-rgt-neg-in_binary64
348×*-commutative_binary64
Counts
75 → 81
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026111
172101
217993
353078
4178978
5352878
6465078
7490178

prune60.0ms (2.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New78381
Fresh000
Picked101
Done000
Total79382
Error
0b
Counts
82 → 3
Alt Table
StatusErrorProgram
21.7b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
20.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 1146 to 891 computations (22.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.1b
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓0.1b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series83.0ms (3.8%)

Counts
2 → 8
Calls

2 calls:

45.0ms
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
38.0ms
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite59.0ms (2.7%)

Algorithm
2×batch-egg-rewrite
Rules
853×log1p-expm1-u_binary64
853×expm1-log1p-u_binary64
415×prod-diff_binary64
85×add-sqr-sqrt_binary64
80×add-log-exp_binary64
Counts
2 → 51
Calls

2 calls:

57.0ms
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
57.0ms
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
117824
2218524
3595924
000
100

simplify95.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
444×distribute-rgt-neg-in_binary64
442×sub-neg_binary64
404×fma-def_binary64
365×distribute-lft-neg-in_binary64
291×cancel-sign-sub-inv_binary64
Counts
59 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
029111
185103
222490
364274
4216474
5439874
6498374
7500074
8493674

prune68.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1040104
Fresh022
Picked011
Done000
Total1043107
Error
0b
Counts
107 → 3
Alt Table
StatusErrorProgram
21.7b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
▶20.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 1457 to 1178 computations (19.1% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.0b
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓0.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series120.0ms (5.5%)

Counts
2 → 4
Calls

2 calls:

74.0ms
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
45.0ms
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite93.0ms (4.3%)

Algorithm
2×batch-egg-rewrite
Rules
791×prod-diff_binary64
301×fma-def_binary64
193×log-div_binary64
175×fma-neg_binary64
166×log1p-udef_binary64
Counts
2 → 81
Calls

2 calls:

92.0ms
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
92.0ms
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
120626
2262726
3491026
4556726
000
100

simplify88.0ms (4%)

Algorithm
1×egg-herbie
Rules
446×distribute-rgt-out--_binary64
394×distribute-rgt-out_binary64
363×distribute-rgt-neg-in_binary64
348×*-commutative_binary64
305×distribute-lft-neg-in_binary64
Counts
85 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02164
15860
214756
343847
4155447
5322247
6463347
7498547
8488447

prune67.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1270127
Fresh011
Picked011
Done011
Total1273130
Error
0b
Counts
130 → 3
Alt Table
StatusErrorProgram
▶21.7b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
✓20.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 2198 to 1571 computations (28.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/8 (pow.f64 x 2))
✓0.0b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))

series6.0ms (0.3%)

Counts
2 → 3
Calls

2 calls:

3.0ms
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
2.0ms
(*.f64 1/8 (pow.f64 x 2))

rewrite54.0ms (2.5%)

Algorithm
2×batch-egg-rewrite
Rules
878×log1p-expm1-u_binary64
878×expm1-log1p-u_binary64
94×add-sqr-sqrt_binary64
90×add-cbrt-cube_binary64
90×add-log-exp_binary64
Counts
2 → 63
Calls

2 calls:

53.0ms
(*.f64 1/8 (pow.f64 x 2))
53.0ms
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
120018
2222918
3519318
000
100

simplify148.0ms (6.7%)

Algorithm
1×egg-herbie
Rules
1127×sqr-pow_binary64
577×fabs-mul_binary64
564×cube-prod_binary64
541×pow-sqr_binary64
523×associate-*l*_binary64
Counts
66 → 66
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
11518
22418
34718
410218
525718
679918
7120218
8130718
9146318
10164318
11182418
12204718
13221418
14263318
15319818
16388418
17410218
18434618
19442818
20446118
21448218
22505118

prune38.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New66066
Fresh000
Picked011
Done022
Total66369
Error
0b
Counts
69 → 3
Alt Table
StatusErrorProgram
✓21.7b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
✓20.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 1237 to 733 computations (40.7% saved)

regimes165.0ms (7.5%)

Accuracy

Total 0.2b remaining (92.5%)

Threshold costs 0.2b (92.5%)

Counts
80 → 1
Compiler

Compiled 2086 to 1676 computations (19.7% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0916
12314
23314
33914
44114
53914

end49.0ms (2.2%)

Compiler

Compiled 56 to 44 computations (21.4% saved)

Profiling

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