Details

Time bar (total: 9.2s)

analyze969.0ms (10.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
0%56.2%43.8%3
0%56.2%43.8%4
3.5%52.7%43.8%5
7%49.2%43.8%6
14%42.1%43.8%7
20.6%35.5%43.8%8
27.4%28.7%43.8%9
29.3%26.9%43.8%10
30.8%25.4%43.8%11
32%24.2%43.8%12
33.5%22.7%43.8%13
34.5%21.6%43.8%14
Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.4s (15.5%)

Symmetry

(sort alpha beta)

Results
1.3s8256×body128valid
Compiler

Compiled 81 to 53 computations (34.6% saved)

simplify215.0ms (2.3%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
2.2b
(/.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)))
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))
Compiler

Compiled 190 to 123 computations (35.3% saved)

localize12.0ms (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)))
14.0b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series303.0ms (3.3%)

Counts
4 → 96
Calls

4 calls:

155.0ms
(/.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)))
74.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
64.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
9.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite75.0ms (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:

21.0ms
(/.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)))
17.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
10.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify207.0ms (2.3%)

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

prune676.0ms (7.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3455350
Fresh101
Picked101
Done000
Total3475352
Error
0b
Counts
352 → 5
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (+.f64 alpha 1) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.3b
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
33.0b
(-.f64 (+.f64 (/.f64 alpha (*.f64 beta beta)) (/.f64 1 (*.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
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)))
2.0b
(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)))))
Compiler

Compiled 21125 to 14318 computations (32.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series263.0ms (2.9%)

Counts
4 → 96
Calls

4 calls:

149.0ms
(/.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)))
71.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
21.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
21.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite83.0ms (0.9%)

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:

26.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
20.0ms
(/.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)))
9.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
7.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

simplify227.0ms (2.5%)

Algorithm
egg-herbie
Rules
940×fma-def_binary64
340×+-commutative_binary64
271×associate-+r+_binary64
244×*-commutative_binary64
216×sub-neg_binary64
Counts
306 → 392
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0107316270
1369615449
2498415449

prune568.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3920392
Fresh044
Picked011
Done000
Total3925397
Error
0b
Counts
397 → 5
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (+.f64 alpha 1) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.3b
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
33.0b
(-.f64 (+.f64 (/.f64 alpha (*.f64 beta beta)) (/.f64 1 (*.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
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)))
2.0b
(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)))))
Compiler

Compiled 22321 to 15102 computations (32.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta)))))
0.0b
(-.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))))
0.1b
(+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha))
1.9b
(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)))))

series144.0ms (1.6%)

Counts
4 → 96
Calls

4 calls:

60.0ms
(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)))))
35.0ms
(-.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))))
25.0ms
(+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha))
23.0ms
(-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta)))))

rewrite49.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
43×add-log-exp_binary64
38×prod-diff_binary64
35×add-sqr-sqrt_binary64
31×add-cube-cbrt_binary64
Counts
4 → 166
Calls

4 calls:

11.0ms
(-.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))))
10.0ms
(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)))))
7.0ms
(-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta)))))
4.0ms
(+.f64 (-.f64 (log1p.f64 beta) (*.f64 2 (log.f64 (+.f64 2 (+.f64 alpha beta))))) (log1p.f64 alpha))

simplify208.0ms (2.3%)

Algorithm
egg-herbie
Rules
905×fma-def_binary64
438×times-frac_binary64
344×sub-neg_binary64
329×+-commutative_binary64
231×cancel-sign-sub-inv_binary64
Counts
262 → 386
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
090115066
1294912611
2519212611

prune942.0ms (10.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3860386
Fresh033
Picked011
Done011
Total3865391
Error
0b
Counts
391 → 5
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (+.f64 alpha 1) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.3b
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
33.0b
(-.f64 (+.f64 (/.f64 alpha (*.f64 beta beta)) (/.f64 1 (*.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
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)))
2.0b
(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)))))
Compiler

Compiled 19772 to 13634 computations (31% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
0.2b
(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3)
14.0b
(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))
20.7b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))

series446.0ms (4.9%)

Counts
4 → 96
Calls

4 calls:

167.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
161.0ms
(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3)
62.0ms
(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))
54.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))

rewrite76.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
42×associate-/r/_binary64
40×*-un-lft-identity_binary64
38×cbrt-prod_binary64
34×flip-+_binary64
34×flip3-+_binary64
Counts
4 → 175
Calls

4 calls:

21.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
15.0ms
(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))
14.0ms
(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3)
8.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))

simplify294.0ms (3.2%)

Algorithm
egg-herbie
Rules
364×+-commutative_binary64
296×associate-+r+_binary64
292×fma-def_binary64
264×*-commutative_binary64
215×associate-*r/_binary64
Counts
271 → 299
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0120418153
1409917116
2506317116

prune648.0ms (7.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2990299
Fresh022
Picked011
Done022
Total2995304
Error
0b
Counts
304 → 5
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (+.f64 alpha 1) (+.f64 beta 1)) (*.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.3b
(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
33.0b
(-.f64 (+.f64 (/.f64 alpha (*.f64 beta beta)) (/.f64 1 (*.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
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)))
2.0b
(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)))))
Compiler

Compiled 20219 to 14294 computations (29.3% saved)

regimes1.0s (11%)

Accuracy

Total 0.1b remaining (69%)

Threshold costs 0.1b (69%)

Counts
252 → 1
Compiler

Compiled 24068 to 17465 computations (27.4% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01740
12740
22640

end279.0ms (3%)

Compiler

Compiled 259 to 178 computations (31.3% saved)

Profiling

Loading profile data...