Details

Time bar (total: 7.7s)

analyze116.0ms (1.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14
Compiler

Compiled 66 to 34 computations (48.5% saved)

sample56.0ms (0.7%)

Algorithm
intervals
Results
27.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 125 to 64 computations (48.8% saved)

simplify48.0ms (0.6%)

Algorithm
egg-herbie
Rules
705×associate-+l+_binary64
492×associate-*l*_binary64
422×associate-*r*_binary64
369×times-frac_binary64
336×associate-/l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01875
16767
229367
3161267
4497967
5503567

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
53.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
53.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
Compiler

Compiled 150 to 66 computations (56% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
0.1b
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
36.6b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
45.7b
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

rewrite690.0ms (8.9%)

Algorithm
rewrite-expression-head
Error
38.9b
Rules
40×add-exp-log_binary64
40×pow1_binary64
31×add-cube-cbrt_binary64
24×add-cbrt-cube_binary64
21×add-sqr-sqrt_binary64
Counts
4 → 191
Calls

4 calls:

133.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
21.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
16.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
14.0ms
(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
Compiler

Compiled 10131 to 3010 computations (70.3% saved)

series1.7s (21.8%)

Error
10.7b
Counts
4 → 89
Calls

4 calls:

1.3s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
154.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
101.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
61.0ms
(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
Compiler

Compiled 22538 to 15057 computations (33.2% saved)

simplify266.0ms (3.4%)

Algorithm
egg-herbie
Rules
708×fma-def_binary64
218×distribute-rgt-in_binary64
202×*-commutative_binary64
200×distribute-lft-in_binary64
186×+-commutative_binary64
Counts
280 → 209
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
072813581
1257512114
2488712114
3496512114

prune166.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2045209
Fresh000
Picked011
Done000
Total2046210
Error
15.8b
Counts
210 → 6
Alt Table
StatusErrorProgram
39.0b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (pow.f64 (+.f64 (fma.f64 i 2 alpha) beta) 2) (fma.f64 i (+.f64 i (+.f64 beta alpha)) (*.f64 beta alpha)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
63.6b
(/.f64 i (/.f64 (*.f64 alpha alpha) (+.f64 i beta)))
58.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3)) (*.f64 9 (/.f64 (*.f64 alpha (*.f64 i i)) (pow.f64 beta 3))))))
56.7b
(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 i alpha)))
22.8b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i)))))
53.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
Compiler

Compiled 10435 to 4226 computations (59.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
0.7b
(/.f64 1/64 (*.f64 i i))
2.5b
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
20.1b
(/.f64 (*.f64 beta beta) (*.f64 i i))

rewrite208.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
10.9b
Rules
34×add-exp-log_binary64
26×add-cbrt-cube_binary64
25×add-cube-cbrt_binary64
23×pow1_binary64
20×add-sqr-sqrt_binary64
Counts
4 → 189
Calls

4 calls:

25.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
20.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
14.0ms
(/.f64 (*.f64 beta beta) (*.f64 i i))
13.0ms
(/.f64 1/64 (*.f64 i i))
Compiler

Compiled 4802 to 1605 computations (66.6% saved)

series97.0ms (1.3%)

Error
10.9b
Counts
4 → 27
Calls

4 calls:

46.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
17.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
17.0ms
(/.f64 (*.f64 beta beta) (*.f64 i i))
6.0ms
(/.f64 1/64 (*.f64 i i))
Compiler

Compiled 1534 to 1093 computations (28.7% saved)

simplify118.0ms (1.5%)

Algorithm
egg-herbie
Rules
406×fma-def_binary64
282×fma-neg_binary64
275×distribute-rgt-in_binary64
258×distribute-lft-in_binary64
221×associate-/l/_binary64
Counts
216 → 110
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01993076
15212434
218932263
348102263
449742263

prune60.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1082110
Fresh134
Picked101
Done011
Total1106116
Error
10.7b
Counts
116 → 6
Alt Table
StatusErrorProgram
58.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3)) (*.f64 9 (/.f64 (*.f64 alpha (*.f64 i i)) (pow.f64 beta 3))))))
56.7b
(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 i alpha)))
39.0b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (pow.f64 (+.f64 (fma.f64 i 2 alpha) beta) 2) (fma.f64 i (+.f64 i (+.f64 beta alpha)) (*.f64 beta alpha)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.5b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))))
53.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.3b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 (/.f64 (*.f64 alpha alpha) (*.f64 i i)) 1/32))
Compiler

Compiled 2040 to 965 computations (52.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.7b
(/.f64 1/64 (*.f64 i i))
2.5b
(/.f64 (*.f64 alpha alpha) (*.f64 i i))

rewrite106.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
10.7b
Rules
18×add-exp-log_binary64
15×add-cube-cbrt_binary64
14×add-cbrt-cube_binary64
times-frac_binary64
pow1_binary64
Counts
2 → 92
Calls

2 calls:

15.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
13.0ms
(/.f64 1/64 (*.f64 i i))
Compiler

Compiled 1620 to 742 computations (54.2% saved)

series27.0ms (0.3%)

Error
10.7b
Counts
2 → 9
Calls

2 calls:

17.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
6.0ms
(/.f64 1/64 (*.f64 i i))
Compiler

Compiled 397 to 309 computations (22.2% saved)

simplify97.0ms (1.3%)

Algorithm
egg-herbie
Rules
481×times-frac_binary64
464×fma-def_binary64
362×unswap-sqr_binary64
323×fma-neg_binary64
305×associate-/l*_binary64
Counts
101 → 54
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
090943
1196756
2515726
32280637
44043637
54943637
64987637

prune48.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New54054
Fresh044
Picked011
Done011
Total54660
Error
10.7b
Counts
60 → 6
Alt Table
StatusErrorProgram
58.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3)) (*.f64 9 (/.f64 (*.f64 alpha (*.f64 i i)) (pow.f64 beta 3))))))
56.7b
(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 i alpha)))
39.0b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (pow.f64 (+.f64 (fma.f64 i 2 alpha) beta) 2) (fma.f64 i (+.f64 i (+.f64 beta alpha)) (*.f64 beta alpha)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.5b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))))
53.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.3b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 (/.f64 (*.f64 alpha alpha) (*.f64 i i)) 1/32))
Compiler

Compiled 1005 to 578 computations (42.5% saved)

localize257.0ms (3.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i))))))
0.7b
(/.f64 1/64 (*.f64 i i))
3.1b
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))
8.8b
(log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))

rewrite372.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
10.7b
Rules
28×add-cube-cbrt_binary64
18×add-cbrt-cube_binary64
18×pow1_binary64
17×add-sqr-sqrt_binary64
16×add-exp-log_binary64
Counts
4 → 149
Calls

4 calls:

228.0ms
(*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i))))))
14.0ms
(/.f64 1/64 (*.f64 i i))
12.0ms
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))
12.0ms
(log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
Compiler

Compiled 3481 to 1589 computations (54.4% saved)

series235.0ms (3%)

Error
10.7b
Counts
4 → 36
Calls

4 calls:

109.0ms
(*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i))))))
62.0ms
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))
45.0ms
(log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
7.0ms
(/.f64 1/64 (*.f64 i i))
Compiler

Compiled 2042 to 1622 computations (20.6% saved)

simplify167.0ms (2.2%)

Algorithm
egg-herbie
Rules
967×fma-def_binary64
540×unswap-sqr_binary64
369×associate-*l*_binary64
329×associate-*r*_binary64
255×log-prod_binary64
Counts
185 → 99
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01832739
13622208
27922046
328062023
440832023
548982023
650512023

prune68.0ms (0.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New99099
Fresh033
Picked011
Done022
Total996105
Error
10.7b
Counts
105 → 6
Alt Table
StatusErrorProgram
58.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3)) (*.f64 9 (/.f64 (*.f64 alpha (*.f64 i i)) (pow.f64 beta 3))))))
56.7b
(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 i alpha)))
39.0b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (pow.f64 (+.f64 (fma.f64 i 2 alpha) beta) 2) (fma.f64 i (+.f64 i (+.f64 beta alpha)) (*.f64 beta alpha)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.5b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 1/32 (exp.f64 (*.f64 2 (log.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))))
53.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.3b
(-.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (*.f64 (/.f64 (*.f64 alpha alpha) (*.f64 i i)) 1/32))
Compiler

Compiled 1685 to 858 computations (49.1% saved)

regimes1.1s (13.7%)

Accuracy

Total 1.6b remaining (13.1%)

Threshold costs 0b (0%)

Compiler

Compiled 22656 to 12585 computations (44.5% saved)

bsearch27.0ms (0.4%)

Steps
ItersRangePoint
5
1.7192133982651408e+108
4.2775248778582753e+108
2.4346701189244063e+108
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02667
12967
22967

end9.0ms (0.1%)

Remove

(sort alpha beta)

Compiler

Compiled 150 to 78 computations (48% saved)

sample1.7s (22%)

Algorithm
intervals
Results
938.0ms8000×body128valid
255.0ms8000×pre128true
Compiler

Compiled 320 to 177 computations (44.7% saved)

Profiling

Loading profile data...