Details

Time bar (total: 9.7s)

analyze4.0ms (0%)

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)

sample177.0ms (1.8%)

Algorithm
intervals
Symmetry

(sort alpha beta)

Results
22.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify215.0ms (2.2%)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
2.6b
(/.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))
2.4b
(/.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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.0b
(*.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)))
19.0b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series307.0ms (3.2%)

Counts
4 → 96
Calls

4 calls:

160.0ms
(/.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)))
79.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
60.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
8.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite80.0ms (0.8%)

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:

22.0ms
(/.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)))
20.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
13.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
11.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify210.0ms (2.1%)

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

prune696.0ms (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3428350
Fresh011
Picked101
Done000
Total3439352
Error
0.0b
Counts
352 → 9
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
2.6b
(/.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))
7.4b
(/.f64 (*.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (*.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)))
2.8b
(/.f64 (/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
3.3b
(*.f64 (*.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
1.8b
(exp.f64 (-.f64 (+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha)) (log.f64 (+.f64 alpha (+.f64 beta 3)))))
3.0b
(*.f64 (/.f64 (+.f64 alpha 1) (*.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))) (/.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))))
30.2b
(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
0.1b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 21499 to 14564 computations (32.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series721.0ms (7.4%)

Counts
4 → 96
Calls

4 calls:

487.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
190.0ms
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
22.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
22.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

rewrite120.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
192×*-un-lft-identity_binary64
89×times-frac_binary64
82×distribute-lft-out_binary64
60×add-sqr-sqrt_binary64
48×add-cube-cbrt_binary64
Counts
4 → 210
Calls

4 calls:

33.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
30.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
23.0ms
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
10.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

simplify231.0ms (2.4%)

Algorithm
egg-herbie
Rules
940×fma-def_binary64
340×+-commutative_binary64
271×associate-+r+_binary64
244×*-commutative_binary64
216×sub-neg_binary64
Counts
306 → 393
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0107316270
1369915449
2498415449

prune880.0ms (9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3867393
Fresh628
Picked101
Done000
Total3939402
Error
0.0b
Counts
402 → 9
Alt Table
StatusErrorProgram
3.3b
(*.f64 (*.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
1.8b
(exp.f64 (-.f64 (+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha)) (log.f64 (+.f64 alpha (+.f64 beta 3)))))
2.4b
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
8.3b
(/.f64 (*.f64 (+.f64 1 alpha) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))
0.2b
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
7.6b
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3) (/.f64 (pow.f64 (+.f64 1 alpha) 3) (pow.f64 (+.f64 2 (+.f64 beta alpha)) 3)))) (+.f64 alpha (+.f64 beta 3)))
0.9b
(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.6b
(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.1b
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 22757 to 15396 computations (32.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series335.0ms (3.4%)

Counts
4 → 96
Calls

4 calls:

173.0ms
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 alpha (+.f64 beta 3)))
79.0ms
(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))))
59.0ms
(/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))
24.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))

rewrite178.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
826×*-un-lft-identity_binary64
508×times-frac_binary64
374×distribute-lft-out_binary64
191×add-sqr-sqrt_binary64
182×add-cube-cbrt_binary64
Counts
4 → 430
Calls

4 calls:

40.0ms
(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))))
28.0ms
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 alpha (+.f64 beta 3)))
17.0ms
(/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))
7.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha)))

simplify376.0ms (3.9%)

Algorithm
egg-herbie
Rules
384×+-commutative_binary64
305×associate-+r+_binary64
291×*-commutative_binary64
271×fma-def_binary64
251×associate-*r/_binary64
Counts
526 → 454
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0122625032
1418423885
2503723885

prune1.0s (10.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4540454
Fresh088
Picked011
Done000
Total4549463
Error
0.0b
Counts
463 → 9
Alt Table
StatusErrorProgram
3.3b
(*.f64 (*.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
1.8b
(exp.f64 (-.f64 (+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha)) (log.f64 (+.f64 alpha (+.f64 beta 3)))))
2.4b
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
8.3b
(/.f64 (*.f64 (+.f64 1 alpha) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))
0.2b
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
7.6b
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3) (/.f64 (pow.f64 (+.f64 1 alpha) 3) (pow.f64 (+.f64 2 (+.f64 beta alpha)) 3)))) (+.f64 alpha (+.f64 beta 3)))
0.9b
(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.6b
(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.1b
(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 alpha (+.f64 beta 3)))
Compiler

Compiled 27149 to 18284 computations (32.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series179.0ms (1.8%)

Counts
2 → 48
Calls

2 calls:

162.0ms
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
16.0ms
(/.f64 1 (+.f64 alpha (+.f64 beta 3)))

rewrite49.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
83×add-exp-log_binary64
56×*-un-lft-identity_binary64
45×add-cbrt-cube_binary64
36×prod-exp_binary64
30×times-frac_binary64
Counts
2 → 115
Calls

2 calls:

26.0ms
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
6.0ms
(/.f64 1 (+.f64 alpha (+.f64 beta 3)))

simplify165.0ms (1.7%)

Algorithm
egg-herbie
Rules
735×times-frac_binary64
607×associate-/l*_binary64
547×fma-def_binary64
187×distribute-rgt-in_binary64
186×+-commutative_binary64
Counts
163 → 204
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06479543
122818670
256218670

prune892.0ms (9.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4173420
Fresh347
Picked011
Done101
Total4218429
Error
0.0b
Counts
429 → 8
Alt Table
StatusErrorProgram
0.2b
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
0.2b
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 3))))))
3.3b
(*.f64 (*.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
1.8b
(exp.f64 (-.f64 (+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha)) (log.f64 (+.f64 alpha (+.f64 beta 3)))))
8.3b
(/.f64 (*.f64 (+.f64 1 alpha) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))
7.4b
(*.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (+.f64 beta 3) alpha) 3))))
0.6b
(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
3.2b
(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (+.f64 1 alpha)) (+.f64 (+.f64 beta 3) alpha)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2)))
Compiler

Compiled 23808 to 16379 computations (31.2% saved)

regimes1.5s (15.1%)

Accuracy

Total 0.1b remaining (78.8%)

Threshold costs 0.1b (78.8%)

Counts
325 → 1
Compiler

Compiled 37511 to 25946 computations (30.8% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
16×+-commutative_binary64
11×*-commutative_binary64
10×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02039
13839
25537
37337
48637
59637
610137
710237
810037

end6.0ms (0.1%)

Remove

(sort alpha beta)

Compiler

Compiled 81 to 54 computations (33.3% saved)

sample1.4s (14%)

Algorithm
intervals
Results
700.0ms8000×body128valid
163.0ms8000×pre128true
Compiler

Compiled 368 to 251 computations (31.8% saved)

Profiling

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