Details

Time bar (total: 1.7min)

analyze52.0ms (0.1%)

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)

sample98.0ms (0.1%)

Algorithm
intervals
Symmetry

(sort alpha beta)

Results
31.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify40.0ms (0%)

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
54.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
54.2b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
Compiler

Compiled 215 to 99 computations (54% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
36.8b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
46.3b
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series3.9s (3.8%)

Counts
4 → 144
Calls

4 calls:

3.5s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
259.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
45.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
16.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite139.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
86×times-frac_binary64
66×associate-/r/_binary64
66×flip-+_binary64
66×flip3-+_binary64
61×add-cbrt-cube_binary64
Counts
4 → 236
Calls

4 calls:

40.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
21.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
11.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
11.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify518.0ms (0.5%)

Algorithm
egg-herbie
Rules
743×fma-def_binary64
533×associate-/l*_binary64
352×times-frac_binary64
64×sub-neg_binary64
59×associate-/l/_binary64
Counts
380 → 516
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0269759448
1566059448

prune1.5s (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New5797586
Fresh000
Picked101
Done000
Total5807587
Error
7.6b
Counts
587 → 7
Alt Table
StatusErrorProgram
59.1b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
58.4b
(/.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)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
15.6b
1/16
54.4b
(/.f64 (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (*.f64 (cbrt.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)) -1)) (cbrt.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)) -1)))) (cbrt.f64 (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1)))
54.3b
(/.f64 (*.f64 (+.f64 i alpha) i) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
37.5b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
39.5b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
Compiler

Compiled 88799 to 46967 computations (47.1% saved)

localize0.0ms (0%)

prune24.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done000
Total077
Error
7.6b
Counts
7 → 7
Alt Table
StatusErrorProgram
59.1b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
58.4b
(/.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)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
15.6b
1/16
54.4b
(/.f64 (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (*.f64 (cbrt.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)) -1)) (cbrt.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)) -1)))) (cbrt.f64 (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1)))
54.3b
(/.f64 (*.f64 (+.f64 i alpha) i) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
37.5b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
39.5b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
Compiler

Compiled 658 to 350 computations (46.8% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))
0.1b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
34.3b
(/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
35.0b
(/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series4.1s (4%)

Counts
4 → 144
Calls

4 calls:

3.5s
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
509.0ms
(/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))
68.0ms
(/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
46.0ms
(/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite219.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
288×times-frac_binary64
200×*-un-lft-identity_binary64
198×add-sqr-sqrt_binary64
117×add-cube-cbrt_binary64
111×associate-*r*_binary64
Counts
4 → 325
Calls

4 calls:

90.0ms
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
20.0ms
(/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))
13.0ms
(/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
6.0ms
(/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify623.0ms (0.6%)

Algorithm
egg-herbie
Rules
820×fma-def_binary64
515×times-frac_binary64
15×cube-mult_binary64
15×unpow3_binary64
12×unpow2_binary64
Counts
469 → 491
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0333972409
1519272409

prune1.6s (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4874491
Fresh325
Picked101
Done011
Total4917498
Error
7.1b
Counts
498 → 7
Alt Table
StatusErrorProgram
59.1b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
58.4b
(/.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)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
53.6b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (+.f64 i alpha) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
38.5b
(*.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))
15.6b
1/16
37.5b
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))
38.0b
(*.f64 (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))))) 1) 1)) (/.f64 (/.f64 (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
Compiler

Compiled 93334 to 56388 computations (39.6% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
0.1b
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))
34.3b
(/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
35.0b
(/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.3min (77.6%)

Counts
2 → 52
Calls

2 calls:

1.3min
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
3.1s
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))

rewrite258.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
276×times-frac_binary64
195×add-sqr-sqrt_binary64
186×*-un-lft-identity_binary64
112×associate-*r*_binary64
105×add-cube-cbrt_binary64
Counts
2 → 258
Calls

2 calls:

93.0ms
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
65.0ms
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))

simplify968.0ms (1%)

Algorithm
egg-herbie
Counts
310 → 254
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07920171203

prune2.9s (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New4670467
Fresh055
Picked011
Done011
Total4677474
Error
7.1b
Counts
474 → 7
Alt Table
StatusErrorProgram
59.1b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
58.4b
(/.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)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
53.6b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (+.f64 i alpha) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
38.5b
(*.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))
15.6b
1/16
37.5b
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))) (/.f64 (/.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))))
38.0b
(*.f64 (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)) (/.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i))))) 1) 1)) (/.f64 (/.f64 (cbrt.f64 (fma.f64 beta alpha (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1)))
Compiler

Compiled 143820 to 92286 computations (35.8% saved)

regimes4.0s (4%)

Accuracy

Total 3.3b remaining (28.2%)

Threshold costs 0b (0%)

Counts
383 → 2
Compiler

Compiled 102484 to 52488 computations (48.8% saved)

bsearch60.0ms (0.1%)

Steps
ItersRangePoint
6
2.2520551222431934e+138
1.1161297287203481e+139
6.876902788558892e+138
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02780
14280
24380
34180

end8.0ms (0%)

Compiler

Compiled 171 to 105 computations (38.6% saved)

sample1.7s (1.7%)

Algorithm
intervals
Results
869.0ms8000×body128valid
208.0ms8000×pre128true
Compiler

Compiled 512 to 271 computations (47.1% saved)

Profiling

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