Details

Time bar (total: 9.4s)

analyze160.0ms (1.7%)

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)

sample2.5s (26.7%)

Results
1.3s6680×body128valid
822.0ms720×body1024valid
219.0ms517×body512valid
76.0ms275×body256valid
40.0ms64×body2048valid
Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify42.0ms (0.5%)

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
18.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶18.6b
(/.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)
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)
Compiler

Compiled 180 to 106 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓11.9b
(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)
✓19.1b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series797.0ms (8.5%)

Counts
3 → 108
Calls

3 calls:

497.0ms
(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)
280.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
19.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

rewrite17.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
7×add-cube-cbrt_binary64
Counts
3 → 67
Calls

3 calls:

8.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
4.0ms
(*.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)

simplify199.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
561×+-commutative_binary64
490×fma-def_binary64
487×associate-+r+_binary64
392×*-commutative_binary64
294×associate-*r/_binary64
Counts
175 → 205
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0140019973
1545019973

prune480.0ms (5.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2005205
Fresh101
Picked101
Done000
Total2025207
Error
0.0b
Counts
207 → 5
Alt Table
StatusErrorProgram
18.7b
(/.f64 (+.f64 (*.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)
55.0b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
50.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶11.9b
(/.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)
53.2b
(/.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)
Compiler

Compiled 25279 to 16306 computations (35.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 beta alpha) (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))))
✓11.9b
(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)

series897.0ms (9.5%)

Counts
3 → 108
Calls

3 calls:

508.0ms
(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)
343.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
45.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

rewrite42.0ms (0.4%)

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:

10.0ms
(/.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)))
0.0ms
(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)

simplify258.0ms (2.7%)

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 → 297
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159125853
1504625853

prune585.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2970297
Fresh044
Picked011
Done000
Total2975302
Error
0.0b
Counts
302 → 5
Alt Table
StatusErrorProgram
▶18.7b
(/.f64 (+.f64 (*.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)
55.0b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
50.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓11.9b
(/.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)
53.2b
(/.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)
Compiler

Compiled 30806 to 19077 computations (38.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓2.7b
(*.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))))))
✓3.5b
(+.f64 (*.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)
19.1b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series741.0ms (7.9%)

Counts
2 → 72
Calls

2 calls:

461.0ms
(+.f64 (*.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)
280.0ms
(*.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))))))

rewrite29.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
11×associate-*r*_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
9×*-un-lft-identity_binary64
9×add-sqr-sqrt_binary64
Counts
2 → 52
Calls

2 calls:

15.0ms
(*.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))))))
10.0ms
(+.f64 (*.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)

simplify245.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
405×+-commutative_binary64
354×fma-def_binary64
349×associate-+r+_binary64
323×*-commutative_binary64
224×associate-*r/_binary64
Counts
124 → 177
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0113518687
1445218582
2498818582

prune707.0ms (7.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3250325
Fresh033
Picked011
Done011
Total3255330
Error
0.0b
Counts
330 → 5
Alt Table
StatusErrorProgram
✓18.7b
(/.f64 (+.f64 (*.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)
55.0b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
▶50.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓11.9b
(/.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)
53.2b
(/.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)
Compiler

Compiled 38651 to 24808 computations (35.8% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

series17.0ms (0.2%)

Counts
1 → 36
Calls

1 calls:

17.0ms
(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64
9×times-frac_binary64
9×add-sqr-sqrt_binary64
9×add-cube-cbrt_binary64
3×associate-/r*_binary64
Counts
1 → 29
Calls

1 calls:

5.0ms
(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

simplify82.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
726×distribute-rgt-in_binary64
711×distribute-lft-in_binary64
389×fma-def_binary64
352×associate-/r/_binary64
323×div-sub_binary64
Counts
65 → 61
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0751277
11321117
23321081
39341079
446761025
548341025
653971025

prune52.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New59261
Fresh112
Picked101
Done022
Total61566
Error
0.0b
Counts
66 → 5
Alt Table
StatusErrorProgram
50.4b
(/.f64 (/.f64 (/.f64 (fma.f64 2 beta (fma.f64 4 i 2)) (*.f64 (cbrt.f64 alpha) (cbrt.f64 alpha))) (cbrt.f64 alpha)) 2)
55.0b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
✓18.7b
(/.f64 (+.f64 (*.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)
✓11.9b
(/.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)
50.1b
(/.f64 (fma.f64 4 (/.f64 i alpha) (/.f64 (fma.f64 2 beta 2) alpha)) 2)
Compiler

Compiled 1603 to 1122 computations (30% saved)

regimes1.2s (13.1%)

Accuracy

Total 1.2b remaining (93%)

Threshold costs 0b (0%)

Counts
109 → 2
Compiler

Compiled 25551 to 18020 computations (29.5% saved)

bsearch5.0ms (0.1%)

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
034107
149107
253107
355107
456107
555107

end251.0ms (2.7%)

Compiler

Compiled 542 to 334 computations (38.4% saved)

Profiling

Loading profile data...