Details

Time bar (total: 18.7s)

analyze5.0ms (0%)

Algorithm
1×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)

sample152.0ms (0.8%)

Algorithm
1×intervals
Symmetry

(sort alpha beta)

Results
21.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify182.0ms (1%)

Algorithm
1×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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.6b
(/.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))
▶1.4b
(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
✓0.0b
(*.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)))
✓16.9b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series275.0ms (1.5%)

Counts
4 → 96
Calls

4 calls:

145.0ms
(/.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)))
71.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
50.0ms
(/.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))

rewrite77.0ms (0.4%)

Algorithm
1×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)))
18.0ms
(*.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)))
10.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify214.0ms (1.1%)

Algorithm
1×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 (6.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New33911350
Fresh101
Picked101
Done000
Total34111352
Error
0.0b
Counts
352 → 11
Alt Table
StatusErrorProgram
1.3b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
1.4b
(/.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 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
2.1b
(*.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)))))
8.5b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.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)))
7.6b
(*.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))) (-.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 3) 2))) (-.f64 alpha (+.f64 beta 3)))
1.7b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
1.3b
(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))))
1.4b
(*.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))))
12.4b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (cbrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (*.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
26.5b
(*.f64 (/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 (+.f64 beta 3) (+.f64 beta 3)) (*.f64 alpha (+.f64 beta 3)))))
Compiler

Compiled 21699 to 14688 computations (32.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓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 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)))

series291.0ms (1.6%)

Counts
4 → 96
Calls

4 calls:

166.0ms
(/.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)))
79.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
24.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
21.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

rewrite87.0ms (0.5%)

Algorithm
1×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:

27.0ms
(*.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)))
8.0ms
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
8.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify270.0ms (1.4%)

Algorithm
1×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

prune975.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3912393
Fresh3710
Picked101
Done000
Total3959404
Error
0.0b
Counts
404 → 9
Alt Table
StatusErrorProgram
1.4b
(*.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))))
▶0.2b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
1.3b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
1.4b
(/.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)))
2.1b
(*.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)))))
8.5b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.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)))
1.3b
(/.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))))
1.7b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
26.5b
(*.f64 (/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 (+.f64 beta 3) (+.f64 beta 3)) (*.f64 alpha (+.f64 beta 3)))))
Compiler

Compiled 22807 to 15420 computations (32.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))))
0.0b
(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
✓0.1b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
✓3.5b
(-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))

series303.0ms (1.6%)

Counts
3 → 72
Calls

3 calls:

213.0ms
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
63.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))))
27.0ms
(-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))

rewrite65.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
41×add-sqr-sqrt_binary64
34×add-cube-cbrt_binary64
26×associate-*l*_binary64
26×times-frac_binary64
Counts
3 → 145
Calls

3 calls:

22.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))))
20.0ms
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
7.0ms
(-.f64 (log1p.f64 beta) (log.f64 (+.f64 2 (+.f64 beta alpha))))

simplify246.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
946×fma-def_binary64
307×+-commutative_binary64
269×*-commutative_binary64
233×associate-+r+_binary64
213×sub-neg_binary64
Counts
217 → 322
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0104816019
1365713903
2503813903

prune1.0s (5.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4063409
Fresh358
Picked101
Done000
Total4108418
Error
0.0b
Counts
418 → 8
Alt Table
StatusErrorProgram
1.7b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (cbrt.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
▶0.1b
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))))
2.5b
(/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (exp.f64 (log1p.f64 beta))) (*.f64 (+.f64 2 (+.f64 alpha beta)) (exp.f64 (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
1.3b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
8.5b
(/.f64 (*.f64 (+.f64 alpha 1) (*.f64 (/.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)))
1.3b
(/.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))))
26.5b
(*.f64 (/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 (+.f64 beta 3) (+.f64 beta 3)) (*.f64 alpha (+.f64 beta 3)))))
1.5b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (log1p.f64 beta))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (exp.f64 (log.f64 (+.f64 2 (+.f64 beta alpha))))))
Compiler

Compiled 26249 to 17940 computations (31.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series196.0ms (1%)

Counts
3 → 72
Calls

3 calls:

155.0ms
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))))
22.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))
18.0ms
(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta))))

rewrite1.9s (9.9%)

Algorithm
1×rewrite-expression-head
Rules
15532×*-un-lft-identity_binary64
12710×times-frac_binary64
6917×distribute-lft-out_binary64
3540×add-sqr-sqrt_binary64
3540×add-cube-cbrt_binary64
Counts
3 → 3924
Calls

3 calls:

93.0ms
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))))
16.0ms
(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta))))
8.0ms
(/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))

simplify3.2s (17%)

Algorithm
1×egg-herbie
Rules
1311×associate-/r/_binary64
978×associate-/l/_binary64
151×fma-def_binary64
60×times-frac_binary64
46×div-sub_binary64
Counts
3996 → 1612
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02198275958
15519275958

prune3.2s (17.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New169361699
Fresh437
Picked101
Done000
Total169891707
Error
0b
Counts
1707 → 9
Alt Table
StatusErrorProgram
2.5b
(/.f64 (/.f64 (*.f64 (+.f64 1 alpha) (exp.f64 (log1p.f64 beta))) (*.f64 (+.f64 2 (+.f64 alpha beta)) (exp.f64 (log.f64 (+.f64 2 (+.f64 beta alpha)))))) (+.f64 alpha (+.f64 beta 3)))
0.1b
(/.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 beta 1))) (+.f64 2 (+.f64 alpha beta)))
4.5b
(*.f64 (*.f64 (sqrt.f64 (+.f64 1 alpha)) (sqrt.f64 (+.f64 beta 1))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 2 (+.f64 alpha beta))))))
1.3b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
1.3b
(/.f64 (+.f64 1 alpha) (*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))) (+.f64 2 (+.f64 alpha beta))))
1.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))) (cbrt.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (*.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))) (+.f64 beta 1))) (/.f64 (cbrt.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))) (/.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (/.f64 1 (+.f64 2 (+.f64 alpha beta))))))
0.2b
(/.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 1 alpha)) (cbrt.f64 (+.f64 1 alpha))) (/.f64 (+.f64 2 (+.f64 beta alpha)) (cbrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 alpha beta)))))
21.3b
(*.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (-.f64 4 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 beta 1) (-.f64 4 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 alpha (+.f64 beta 3))) (-.f64 2 (+.f64 alpha beta)))))
1.5b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (exp.f64 (log1p.f64 beta))) (*.f64 (+.f64 alpha (+.f64 beta 3)) (exp.f64 (log.f64 (+.f64 2 (+.f64 beta alpha))))))
Compiler

Compiled 95878 to 62833 computations (34.5% saved)

regimes3.4s (18.3%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts
662 → 1
Compiler

Compiled 80804 to 56444 computations (30.1% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
12537
22437

end7.0ms (0%)

Compiler

Compiled 81 to 54 computations (33.3% saved)

sample1.4s (7.3%)

Algorithm
1×intervals
Results
641.0ms8000×body128valid
160.0ms8000×pre128true
Compiler

Compiled 420 to 285 computations (32.1% saved)

Profiling

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