Details

Time bar (total: 15.1s)

analyze156.0ms (1%)

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6
Compiler

Compiled 44 to 29 computations (34.1% saved)

sample82.0ms (0.5%)

Algorithm
intervals
Results
41.0ms256×body128valid
9.0ms256×pre128true
Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify221.0ms (1.5%)

Algorithm
egg-herbie
Rules
1227×associate-/l*_binary64
689×distribute-rgt-in_binary64
661×distribute-lft-in_binary64
481×associate-/l/_binary64
450×associate-*l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01540
13638
211438
346837
4235937
5233037
6245837
7271737
8306737
9303837
10313637
11326337
12340637
13370637
14427337
15408437
16410737
17411437
18412137
19412837
20413537
21414237
22414937
23415637
24522637

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
4.4b
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
1.9b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 190 to 123 computations (35.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
18.8b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series555.0ms (3.7%)

Counts
4 → 96
Calls

4 calls:

294.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
148.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
97.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
15.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite159.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity_binary64
34×distribute-lft-out_binary64
34×add-cbrt-cube_binary64
34×add-exp-log_binary64
24×flip-+_binary64
Counts
4 → 166
Calls

4 calls:

42.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
37.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
28.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
23.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify408.0ms (2.7%)

Algorithm
egg-herbie
Rules
363×+-commutative_binary64
342×distribute-rgt-in_binary64
291×associate-+r+_binary64
266×fma-def_binary64
257×*-commutative_binary64
Counts
262 → 350
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0106115235
1371914320
2514114320

prune1.3s (8.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3437350
Fresh101
Picked101
Done000
Total3457352
Error
0.0b
Counts
352 → 7
Alt Table
StatusErrorProgram
1.9b
(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
2.0b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
1.9b
(/.f64 (+.f64 alpha 1) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))
30.0b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 (+.f64 1 beta) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4))) (*.f64 (-.f64 (+.f64 alpha beta) 2) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
27.4b
(-.f64 (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 1 (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 beta (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (fma.f64 3 (/.f64 (*.f64 alpha (pow.f64 beta 3)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 30 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (*.f64 17 (/.f64 (*.f64 alpha (*.f64 beta beta)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
8.3b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (/.f64 (*.f64 (+.f64 2 (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4)) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 21477 to 14556 computations (32.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0b
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b
(*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

series533.0ms (3.5%)

Counts
4 → 96
Calls

4 calls:

318.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
140.0ms
(*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))
45.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
28.0ms
(/.f64 1 (+.f64 (+.f64 alpha beta) 2))

rewrite159.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
97×*-un-lft-identity_binary64
85×add-exp-log_binary64
51×add-cbrt-cube_binary64
40×distribute-lft-out_binary64
40×times-frac_binary64
Counts
4 → 184
Calls

4 calls:

47.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
38.0ms
(*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))
15.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms
(/.f64 1 (+.f64 (+.f64 alpha beta) 2))

simplify412.0ms (2.7%)

Algorithm
egg-herbie
Rules
951×fma-def_binary64
339×+-commutative_binary64
268×associate-+r+_binary64
242×*-commutative_binary64
196×sub-neg_binary64
Counts
280 → 369
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0105315028
1359114068
2504914068

prune1.4s (9.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3654369
Fresh336
Picked101
Done000
Total3697376
Error
0.0b
Counts
376 → 7
Alt Table
StatusErrorProgram
0.2b
(*.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
0.5b
(/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
30.0b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 (+.f64 1 beta) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4))) (*.f64 (-.f64 (+.f64 alpha beta) 2) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
1.9b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 1 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
27.4b
(-.f64 (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 1 (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 beta (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (fma.f64 3 (/.f64 (*.f64 alpha (pow.f64 beta 3)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 30 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (*.f64 17 (/.f64 (*.f64 alpha (*.f64 beta beta)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
2.0b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 21740 to 15000 computations (31% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2))
0.1b
(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))
0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))

series487.0ms (3.2%)

Counts
3 → 72
Calls

3 calls:

306.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
136.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2))
44.0ms
(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))

rewrite166.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
157×*-un-lft-identity_binary64
107×times-frac_binary64
70×distribute-lft-out_binary64
64×add-exp-log_binary64
46×add-sqr-sqrt_binary64
Counts
3 → 202
Calls

3 calls:

43.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
43.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2))
24.0ms
(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))

simplify452.0ms (3%)

Algorithm
egg-herbie
Rules
921×fma-def_binary64
313×+-commutative_binary64
249×associate-+r+_binary64
242×*-commutative_binary64
175×sub-neg_binary64
Counts
274 → 368
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0105016466
1360915649
2499115649

prune1.0s (6.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4442446
Fresh246
Picked011
Done000
Total4467453
Error
0.0b
Counts
453 → 7
Alt Table
StatusErrorProgram
0.5b
(/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
30.0b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 (+.f64 1 beta) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4))) (*.f64 (-.f64 (+.f64 alpha beta) 2) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
1.9b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 1 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
27.4b
(-.f64 (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 1 (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 beta (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (fma.f64 3 (/.f64 (*.f64 alpha (pow.f64 beta 3)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 30 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (*.f64 17 (/.f64 (*.f64 alpha (*.f64 beta beta)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
0.2b
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha)))
0.8b
(*.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (*.f64 (cbrt.f64 (+.f64 (+.f64 beta 3) alpha)) (cbrt.f64 (+.f64 (+.f64 beta 3) alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (cbrt.f64 (+.f64 (+.f64 beta 3) alpha))))
0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 25492 to 17343 computations (32% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))
0.1b
(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))
0.1b
(/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha))
0.1b
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha)))

series791.0ms (5.2%)

Counts
4 → 64
Calls

4 calls:

347.0ms
(/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha))
250.0ms
(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))
167.0ms
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha)))
26.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))

rewrite177.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
330×*-un-lft-identity_binary64
229×times-frac_binary64
148×sqrt-prod_binary64
147×distribute-lft-out_binary64
100×add-sqr-sqrt_binary64
Counts
4 → 291
Calls

4 calls:

66.0ms
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha)))
23.0ms
(/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha))
15.0ms
(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))
11.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))

simplify362.0ms (2.4%)

Algorithm
egg-herbie
Rules
309×*-commutative_binary64
283×+-commutative_binary64
216×associate-+r+_binary64
216×fma-def_binary64
169×associate-*r/_binary64
Counts
355 → 405
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0110424254
1367223252
2499423252

prune1.3s (8.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New5142516
Fresh145
Picked011
Done011
Total5158523
Error
0.0b
Counts
523 → 8
Alt Table
StatusErrorProgram
29.7b
(*.f64 (/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (+.f64 (pow.f64 (+.f64 beta 3) 3) (pow.f64 alpha 3))) (+.f64 (*.f64 (+.f64 beta 3) (+.f64 beta 3)) (-.f64 (*.f64 alpha alpha) (*.f64 (+.f64 beta 3) alpha))))
0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
0.5b
(/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
30.0b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 (+.f64 1 beta) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4))) (*.f64 (-.f64 (+.f64 alpha beta) 2) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
1.9b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 1 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
27.4b
(-.f64 (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 1 (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 beta (*.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (fma.f64 3 (/.f64 (*.f64 alpha (pow.f64 beta 3)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 30 (/.f64 (*.f64 alpha beta) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (fma.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))) (*.f64 17 (/.f64 (*.f64 alpha (*.f64 beta beta)) (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
0.2b
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 beta 3) alpha)))
0.7b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))) (fabs.f64 (cbrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))) (/.f64 (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))) (+.f64 (+.f64 beta 3) alpha)))
Compiler

Compiled 40891 to 27350 computations (33.1% saved)

regimes3.3s (22.2%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts
486 → 1
Compiler

Compiled 67667 to 46811 computations (30.8% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01849
12949
22849

end8.0ms (0.1%)

Remove

(sort alpha beta)

Compiler

Compiled 105 to 69 computations (34.3% saved)

sample1.4s (9.3%)

Algorithm
intervals
Results
697.0ms8000×body128valid
163.0ms8000×pre128true
Compiler

Compiled 511 to 348 computations (31.9% saved)

Profiling

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