Details

Time bar (total: 21.2s)

analyze111.0ms (0.5%)

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 67 to 35 computations (47.8% saved)

sample59.0ms (0.3%)

Algorithm
intervals
Results
31.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify40.0ms (0.2%)

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 → 2
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
New112
Fresh101
Picked000
Done000
Total213
Error
55.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
55.0b
(/.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 203 to 89 computations (56.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)))
34.0b
(/.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))
47.3b
(/.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))))

series3.1s (14.6%)

Counts
4 → 144
Calls

4 calls:

2.7s
(/.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))
275.0ms
(/.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))))
48.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
17.0ms
(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite53.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube_binary64
61×add-exp-log_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
21×add-sqr-sqrt_binary64
Counts
4 → 132
Calls

4 calls:

11.0ms
(/.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))
9.0ms
(/.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))))
7.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
3.0ms
(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify447.0ms (2.1%)

Algorithm
egg-herbie
Rules
740×fma-def_binary64
507×associate-/l*_binary64
344×times-frac_binary64
54×sqr-pow_binary64
54×sub-neg_binary64
Counts
276 → 296
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0256648816
1515848816

prune1.4s (6.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New28511296
Fresh000
Picked011
Done000
Total28512297
Error
7.1b
Counts
297 → 12
Alt Table
StatusErrorProgram
55.2b
(exp.f64 (log.f64 (/.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))))
55.0b
(/.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))
37.4b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
58.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.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))
37.4b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
55.1b
(/.f64 (*.f64 (*.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))
37.4b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
37.8b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
54.6b
(/.f64 (-.f64 (fma.f64 i alpha (*.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (*.f64 (*.f64 i i) alpha) beta) (/.f64 (*.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
63.5b
(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
39.9b
(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.6b
1/16
Compiler

Compiled 63977 to 36855 computations (42.4% saved)

localize0.0ms (0%)

prune17.0ms (0.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New000
Fresh01010
Picked011
Done011
Total01212
Error
7.1b
Counts
12 → 12
Alt Table
StatusErrorProgram
55.2b
(exp.f64 (log.f64 (/.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))))
55.0b
(/.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))
37.4b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
58.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.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))
37.4b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
55.1b
(/.f64 (*.f64 (*.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))
37.4b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
37.8b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
54.6b
(/.f64 (-.f64 (fma.f64 i alpha (*.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (*.f64 (*.f64 i i) alpha) beta) (/.f64 (*.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
63.5b
(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
39.9b
(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.6b
1/16
Compiler

Compiled 1144 to 522 computations (54.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
31.6b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
33.1b
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
34.0b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))

series3.2s (14.9%)

Counts
4 → 144
Calls

4 calls:

2.8s
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
284.0ms
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
68.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
46.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite60.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube_binary64
61×add-exp-log_binary64
30×add-sqr-sqrt_binary64
28×times-frac_binary64
25×*-un-lft-identity_binary64
Counts
4 → 138
Calls

4 calls:

14.0ms
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
13.0ms
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
7.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
2.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify525.0ms (2.5%)

Algorithm
egg-herbie
Rules
748×fma-def_binary64
557×associate-/l*_binary64
346×times-frac_binary64
84×sub-neg_binary64
56×sqr-pow_binary64
Counts
282 → 329
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0279450455
1549750455

prune1.2s (5.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3245329
Fresh459
Picked101
Done112
Total33011341
Error
7.1b
Counts
341 → 11
Alt Table
StatusErrorProgram
37.8b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
37.4b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
58.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.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))
39.2b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (expm1.f64 (log1p.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
37.5b
(/.f64 (*.f64 (*.f64 (/.f64 i (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
37.7b
(exp.f64 (log.f64 (/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))))
37.4b
(/.f64 (*.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
63.5b
(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
37.4b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
39.9b
(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.6b
1/16
Compiler

Compiled 68505 to 39311 computations (42.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta))))
0.3b
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))
33.1b
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
34.0b
(/.f64 (*.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))

series3.6s (17%)

Counts
3 → 108
Calls

3 calls:

3.5s
(/.f64 (*.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
83.0ms
(/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta))))
61.0ms
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))

rewrite130.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
153×*-un-lft-identity_binary64
141×times-frac_binary64
73×add-sqr-sqrt_binary64
73×add-cube-cbrt_binary64
48×distribute-lft-out_binary64
Counts
3 → 179
Calls

3 calls:

30.0ms
(/.f64 (*.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
17.0ms
(/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta))))
11.0ms
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))

simplify833.0ms (3.9%)

Algorithm
egg-herbie
Rules
561×fma-def_binary64
444×associate-/l*_binary64
357×associate-/r*_binary64
346×times-frac_binary64
71×associate-/r/_binary64
Counts
287 → 316
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0236242749
1544642749

prune1.2s (5.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3864390
Fresh549
Picked101
Done011
Total3929401
Error
7.1b
Counts
401 → 9
Alt Table
StatusErrorProgram
37.8b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
37.4b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
63.5b
(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
37.8b
(/.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i)) (/.f64 (cbrt.f64 i) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta))))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
37.4b
(/.f64 (*.f64 (*.f64 (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 i (/.f64 1 (+.f64 i (+.f64 alpha beta))))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.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))
39.9b
(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
17.6b
1/16
37.4b
(/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
58.0b
(/.f64 (*.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (+.f64 i (+.f64 alpha beta)))) (/.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
Compiler

Compiled 66281 to 36428 computations (45% saved)

regimes2.9s (13.8%)

Accuracy

Total 2.9b remaining (22.5%)

Threshold costs 0b (0%)

Counts
199 → 2
Compiler

Compiled 60884 to 31753 computations (47.8% saved)

bsearch37.0ms (0.2%)

Steps
ItersRangePoint
3
4.560829120505558e+129
5.4285625511200786e+129
5.3743292117066705e+129
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02569
13269
23269

end40.0ms (0.2%)

Compiler

Compiled 153 to 87 computations (43.1% saved)

sample2.2s (10.3%)

Algorithm
intervals
Results
1.0s8000×body128valid
227.0ms8000×pre128true
Compiler

Compiled 507 to 250 computations (50.7% saved)

Profiling

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