Details

Time bar (total: 16.2s)

analyze167.0ms (1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 43 to 28 computations (34.9% saved)

sample2.2s (13.4%)

Results
1.3s6717×body128valid
372.0ms692×body1024valid
211.0ms515×body512valid
136.0ms44×body2048valid
78.0ms288×body256valid
Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify43.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
847×times-frac_binary64
817×distribute-rgt-in_binary64
748×distribute-lft-in_binary64
537×div-sub_binary64
535×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01643
13439
211037
343537
4167237
5249437
6335837
7539237

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
19.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
25.0b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
▶19.9b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 180 to 106 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
✓0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓11.8b
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓18.7b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series805.0ms (5%)

Counts
4 → 144
Calls

4 calls:

483.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
293.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
21.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
7.0ms
(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
17×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
9×add-cube-cbrt_binary64
Counts
4 → 85
Calls

4 calls:

8.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
5.0ms
(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
5.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify656.0ms (4%)

Algorithm
1×egg-herbie
Rules
563×+-commutative_binary64
490×fma-def_binary64
488×associate-+r+_binary64
393×*-commutative_binary64
294×associate-*r/_binary64
Counts
229 → 235
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0141020564
1547420564

prune565.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2314235
Fresh011
Picked101
Done000
Total2325237
Error
0.1b
Counts
237 → 5
Alt Table
StatusErrorProgram
25.0b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
51.1b
(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
▶11.7b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
52.1b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
50.2b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 25668 to 16444 computations (35.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
✓0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓0.3b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓11.8b
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series909.0ms (5.6%)

Counts
3 → 108
Calls

3 calls:

534.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)
327.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
47.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

rewrite40.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
166×times-frac_binary64
156×*-un-lft-identity_binary64
116×add-sqr-sqrt_binary64
78×add-cube-cbrt_binary64
24×associate-/l*_binary64
Counts
3 → 169
Calls

3 calls:

11.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
5.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
1.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

simplify295.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
490×fma-def_binary64
477×associate-+r+_binary64
326×associate-*r/_binary64
177×associate-/l*_binary64
171×associate-/r*_binary64
Counts
277 → 298
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159125853
1504625853

prune768.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3271328
Fresh044
Picked101
Done000
Total3285333
Error
0.1b
Counts
333 → 5
Alt Table
StatusErrorProgram
▶11.9b
(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
25.0b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
51.1b
(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
52.1b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
50.2b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 31256 to 19249 computations (38.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))
0.3b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓3.2b
(log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))
11.8b
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series3.3s (20.1%)

Counts
2 → 72
Calls

2 calls:

2.8s
(log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))
499.0ms
(exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
6×log-prod_binary64
5×*-un-lft-identity_binary64
5×add-sqr-sqrt_binary64
5×add-cube-cbrt_binary64
4×exp-prod_binary64
Counts
2 → 31
Calls

2 calls:

2.0ms
(exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))
1.0ms
(log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))

simplify351.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
826×fma-def_binary64
426×associate-/r*_binary64
392×associate-/l*_binary64
362×times-frac_binary64
59×sqr-pow_binary64
Counts
103 → 140
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0238941564
1551041564

prune1.4s (8.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2772279
Fresh134
Picked011
Done000
Total2786284
Error
0.1b
Counts
284 → 6
Alt Table
StatusErrorProgram
✓11.9b
(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
51.1b
(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
▶25.3b
(/.f64 (exp.f64 (log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))))) 2)
55.8b
(/.f64 (exp.f64 (-.f64 (fma.f64 16 (/.f64 beta (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 744 (/.f64 (*.f64 (*.f64 beta beta) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 152 (/.f64 (*.f64 beta beta) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 100 (/.f64 (pow.f64 beta 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 224 (/.f64 i (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 672 (/.f64 (*.f64 i i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (+.f64 (neg.f64 (log.f64 alpha)) (fma.f64 4 (/.f64 (pow.f64 beta 5) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 672 (/.f64 (*.f64 beta i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 1920 (/.f64 (*.f64 beta (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 48 (/.f64 (*.f64 beta i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 880 (/.f64 (*.f64 (*.f64 beta beta) (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 32 (/.f64 (pow.f64 i 3) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 32 (/.f64 1 (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 32 (/.f64 (pow.f64 beta 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (+.f64 (log.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i)))) (fma.f64 112 (/.f64 beta (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 1320 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 10 (/.f64 (*.f64 beta beta) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 32 (/.f64 i (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 2 (/.f64 (pow.f64 beta 3) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 8 (/.f64 1 (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 20 (/.f64 (*.f64 (*.f64 beta beta) i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 960 (/.f64 (*.f64 beta (pow.f64 i 4)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 48 (/.f64 (*.f64 i i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (*.f64 alpha alpha))) (fma.f64 64 (/.f64 (*.f64 (pow.f64 beta 4) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 384 (/.f64 (pow.f64 i 5) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 360 (/.f64 (*.f64 (pow.f64 beta 3) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 1632 (/.f64 (*.f64 beta (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 960 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (fma.f64 1088 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3))) (*.f64 360 (/.f64 (*.f64 (pow.f64 beta 3) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (pow.f64 alpha 3)))))))))))))))))))))))))))))))))))) (fma.f64 176 (/.f64 (*.f64 beta beta) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 1728 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 96 (/.f64 (*.f64 (*.f64 beta beta) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 40 (/.f64 beta (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 768 (/.f64 (*.f64 i i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 2592 (/.f64 (*.f64 beta (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 24 (/.f64 (pow.f64 beta 5) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 26 (/.f64 (*.f64 beta beta) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 12 (/.f64 (pow.f64 beta 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 48 (/.f64 i (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 4032 (/.f64 (*.f64 (*.f64 beta beta) (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 6 (/.f64 beta (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 120 (/.f64 (*.f64 i i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 3216 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 1728 (/.f64 (*.f64 (pow.f64 beta 3) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 168 (/.f64 (pow.f64 beta 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 120 (/.f64 (*.f64 beta i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 144 (/.f64 (*.f64 beta (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 88 (/.f64 (pow.f64 beta 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 1728 (/.f64 (*.f64 beta (pow.f64 i 5)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 160 (/.f64 (*.f64 beta i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 1200 (/.f64 (*.f64 (*.f64 beta beta) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 96 (/.f64 beta (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 2 (/.f64 (pow.f64 beta 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 160 (/.f64 (pow.f64 i 3) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 4608 (/.f64 (*.f64 beta (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 24 (/.f64 beta (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 8 (/.f64 1 (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 96 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 4 (/.f64 1 (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 64/3 (/.f64 1 (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 1152 (/.f64 (*.f64 (pow.f64 beta 3) (pow.f64 i 3)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 576 (/.f64 (pow.f64 i 6) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 192 (/.f64 i (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 36 (/.f64 (*.f64 beta beta) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 80 (/.f64 i (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 336 (/.f64 (*.f64 (pow.f64 beta 4) (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 2 (/.f64 (pow.f64 beta 4) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 14 (/.f64 (pow.f64 beta 3) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 16 (/.f64 1 (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 2 (/.f64 (*.f64 beta beta) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 48 (/.f64 (*.f64 (pow.f64 beta 5) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 912 (/.f64 (*.f64 (pow.f64 beta 3) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 28 (/.f64 (*.f64 (pow.f64 beta 3) i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 80 (/.f64 (pow.f64 i 4) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 336 (/.f64 (*.f64 (pow.f64 beta 4) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 8/3 (/.f64 (pow.f64 beta 6) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 160 (/.f64 (*.f64 i i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) (pow.f64 alpha 3))) (fma.f64 12 (/.f64 (*.f64 beta i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 24 (/.f64 (*.f64 (pow.f64 beta 3) i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 72 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 216 (/.f64 (*.f64 beta (*.f64 i i)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (fma.f64 12 (/.f64 i (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 1728 (/.f64 (pow.f64 i 5) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 2304 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 2016 (/.f64 (*.f64 (*.f64 beta beta) (pow.f64 i 4)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) alpha)) (fma.f64 768 (/.f64 (*.f64 beta i) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))) (fma.f64 144 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 2) (*.f64 alpha alpha))) (*.f64 4320 (/.f64 (*.f64 beta (pow.f64 i 4)) (*.f64 (pow.f64 (fma.f64 2 beta (+.f64 2 (*.f64 4 i))) 3) (pow.f64 alpha 3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2)
52.1b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
50.2b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 74250 to 50911 computations (31.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(exp.f64 (log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))))
✓1.6b
(-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))
✓2.2b
(log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))))
✓18.4b
(/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))

series306.0ms (1.9%)

Counts
4 → 96
Calls

4 calls:

168.0ms
(log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))))
46.0ms
(-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))
46.0ms
(exp.f64 (log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))))
45.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))

rewrite42.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
29×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
21×prod-diff_binary64
20×add-cube-cbrt_binary64
17×add-exp-log_binary64
Counts
4 → 121
Calls

4 calls:

8.0ms
(/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))
6.0ms
(log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))))
5.0ms
(-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))
5.0ms
(exp.f64 (log.f64 (-.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))))

simplify419.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
829×times-frac_binary64
799×fma-def_binary64
217×+-commutative_binary64
175×*-commutative_binary64
170×associate-+r+_binary64
Counts
217 → 246
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
077414297
1245613525
2497313485
3500013485
4496613485

prune532.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2442246
Fresh134
Picked101
Done011
Total2466252
Error
0.1b
Counts
252 → 6
Alt Table
StatusErrorProgram
✓11.9b
(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
51.1b
(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
25.3b
(/.f64 (exp.f64 (-.f64 (log.f64 (-.f64 (pow.f64 1 3) (pow.f64 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))) 3))) (log.f64 (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))) (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha))))) (*.f64 1 (/.f64 (*.f64 alpha alpha) (*.f64 (fma.f64 2 i alpha) (+.f64 2 (fma.f64 2 i alpha)))))))))) 2)
52.1b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
50.2b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
56.3b
(/.f64 (exp.f64 (-.f64 (fma.f64 384 (/.f64 (pow.f64 i 5) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))) (+.f64 (fma.f64 32 (/.f64 i (*.f64 (*.f64 alpha alpha) (fma.f64 i 4 2))) (log.f64 (fma.f64 i 4 2))) (fma.f64 224 (/.f64 i (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 1088 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 48 (/.f64 (*.f64 i i) (*.f64 (*.f64 alpha alpha) (fma.f64 i 4 2))) (-.f64 (fma.f64 960 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 32 (/.f64 (pow.f64 i 3) (*.f64 (*.f64 alpha alpha) (fma.f64 i 4 2))) (+.f64 (/.f64 8 (*.f64 (*.f64 alpha alpha) (fma.f64 i 4 2))) (fma.f64 672 (/.f64 (*.f64 i i) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))) (/.f64 32 (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 2))))))) (log.f64 alpha))))))) (+.f64 (/.f64 4 (*.f64 alpha (fma.f64 i 4 2))) (fma.f64 80 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 alpha 3) (fma.f64 i 4 2))) (fma.f64 12 (/.f64 i (*.f64 alpha (fma.f64 i 4 2))) (fma.f64 1728 (/.f64 (pow.f64 i 5) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (fma.f64 80 (/.f64 i (*.f64 (pow.f64 alpha 3) (fma.f64 i 4 2))) (fma.f64 2304 (/.f64 (pow.f64 i 4) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (fma.f64 160 (/.f64 (*.f64 i i) (*.f64 (pow.f64 alpha 3) (fma.f64 i 4 2))) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha (fma.f64 i 4 2))) (fma.f64 144 (/.f64 (pow.f64 i 3) (*.f64 (*.f64 alpha alpha) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 48 (/.f64 i (*.f64 (*.f64 alpha alpha) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 768 (/.f64 (*.f64 i i) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (+.f64 (/.f64 8 (*.f64 (*.f64 alpha alpha) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 72 (/.f64 (pow.f64 i 4) (*.f64 (*.f64 alpha alpha) (pow.f64 (fma.f64 i 4 2) 2))) (fma.f64 160 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 alpha 3) (fma.f64 i 4 2))) (fma.f64 576 (/.f64 (pow.f64 i 6) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (fma.f64 192 (/.f64 i (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (+.f64 (/.f64 16 (*.f64 (pow.f64 alpha 3) (fma.f64 i 4 2))) (+.f64 (/.f64 64/3 (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))) (fma.f64 120 (/.f64 (*.f64 i i) (*.f64 (*.f64 alpha alpha) (pow.f64 (fma.f64 i 4 2) 2))) (*.f64 1728 (/.f64 (pow.f64 i 3) (*.f64 (pow.f64 alpha 3) (pow.f64 (fma.f64 i 4 2) 3))))))))))))))))))))))))) 2)
Compiler

Compiled 16885 to 12134 computations (28.1% saved)

regimes3.0s (18.8%)

Accuracy

Total 1.3b remaining (92.2%)

Threshold costs 0b (0%)

Counts
184 → 2
Compiler

Compiled 75439 to 54925 computations (27.2% saved)

bsearch16.0ms (0.1%)

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
032100
144100
248100
350100
451100
550100

end364.0ms (2.2%)

Compiler

Compiled 793 to 544 computations (31.4% saved)

Profiling

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