Details

Time bar (total: 6.8s)

analyze288.0ms (4.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
28.1%28.1%43.8%2
56.2%0%43.8%3
Compiler

Compiled 22 to 16 computations (27.3% saved)

sample38.0ms (0.6%)

Algorithm
intervals
Results
8.0ms183×body128valid
8.0ms256×pre128true
6.0ms40×body1024valid
2.0ms20×body512valid
1.0msbody2048valid
1.0msbody256valid
Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify228.0ms (3.4%)

Algorithm
egg-herbie
Rules
1179×div-sub_binary64
672×sub-neg_binary64
434×cancel-sign-sub-inv_binary64
422×associate-/l*_binary64
385×distribute-rgt-neg-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
12319
23919
36319
410419
520419
632019
751319
894319
9208719
10293019
11370519
12390619
13407719
14416519
15419819
16420019
17432019
18459419
19469819
20469819
21501819

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
17.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
17.8b
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
Compiler

Compiled 45 to 33 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.4b
(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite83.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
17.1b
Rules
58×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
25×times-frac_binary64
19×distribute-lft-out_binary64
14×add-cube-cbrt_binary64
Counts
2 → 65
Calls

2 calls:

15.0ms
(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
Compiler

Compiled 1149 to 611 computations (46.8% saved)

series117.0ms (1.7%)

Error
0.0b
Counts
2 → 38
Calls

2 calls:

53.0ms
(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
37.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
Compiler

Compiled 2608 to 2048 computations (21.5% saved)

simplify117.0ms (1.7%)

Algorithm
egg-herbie
Rules
484×times-frac_binary64
453×distribute-rgt-in_binary64
389×distribute-lft-in_binary64
290×cancel-sign-sub-inv_binary64
258×sub-neg_binary64
Counts
103 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02293134
16443099
220612961
346382955
449612955

prune63.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New89392
Fresh000
Picked011
Done000
Total89493
Error
0.0b
Counts
93 → 4
Alt Table
StatusErrorProgram
17.8b
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
45.5b
(/.f64 (+.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (*.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))) (*.f64 (/.f64 beta alpha) (+.f64 2 (/.f64 16 (*.f64 alpha alpha))))))) (-.f64 (*.f64 2 (pow.f64 (/.f64 beta alpha) 3)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
44.7b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (*.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)
33.7b
(/.f64 (/.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 2)
Compiler

Compiled 2025 to 1255 computations (38% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
0.0b
(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
1.6b
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
3.0b
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))

rewrite262.0ms (3.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
501×*-un-lft-identity_binary64
220×times-frac_binary64
161×distribute-lft-out_binary64
149×add-sqr-sqrt_binary64
83×swap-sqr_binary64
Counts
4 → 232
Calls

4 calls:

39.0ms
(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
18.0ms
(/.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
15.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
3.0ms
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
Compiler

Compiled 7182 to 4112 computations (42.7% saved)

series853.0ms (12.6%)

Error
0.0b
Counts
4 → 62
Calls

4 calls:

605.0ms
(/.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
70.0ms
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
48.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
36.0ms
(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
Compiler

Compiled 13435 to 10454 computations (22.2% saved)

simplify304.0ms (4.5%)

Algorithm
egg-herbie
Rules
867×times-frac_binary64
206×*-commutative_binary64
187×+-commutative_binary64
178×distribute-rgt-in_binary64
168×distribute-lft-in_binary64
Counts
294 → 222
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
077417172
1266016445
2505616445

prune153.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2211222
Fresh022
Picked101
Done011
Total2224226
Error
0.0b
Counts
226 → 4
Alt Table
StatusErrorProgram
17.8b
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
45.5b
(/.f64 (+.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (*.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))) (*.f64 (/.f64 beta alpha) (+.f64 2 (/.f64 16 (*.f64 alpha alpha))))))) (-.f64 (*.f64 2 (pow.f64 (/.f64 beta alpha) 3)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
44.7b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (*.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)
33.7b
(/.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3)) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 2)
Compiler

Compiled 7684 to 4916 computations (36% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3)
0.1b
(cbrt.f64 (pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3))
1.6b
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
3.0b
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))

rewrite115.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×cbrt-prod_binary64
12×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
add-log-exp_binary64
Counts
4 → 72
Calls

4 calls:

14.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
5.0ms
(pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3)
4.0ms
(cbrt.f64 (pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3))
3.0ms
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
Compiler

Compiled 3651 to 2216 computations (39.3% saved)

series349.0ms (5.2%)

Error
0.0b
Counts
4 → 53
Calls

4 calls:

127.0ms
(pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3)
66.0ms
(+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
64.0ms
(cbrt.f64 (pow.f64 (+.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 3))
48.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
Compiler

Compiled 6733 to 5151 computations (23.5% saved)

simplify182.0ms (2.7%)

Algorithm
egg-herbie
Rules
351×unswap-sqr_binary64
307×sub-neg_binary64
261×associate-+r+_binary64
225×+-commutative_binary64
174×associate-+l+_binary64
Counts
125 → 98
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03486756
19826195
236826126
348556126
449296126

prune72.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New97198
Fresh022
Picked101
Done011
Total984102
Error
0.0b
Counts
102 → 4
Alt Table
StatusErrorProgram
17.8b
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
33.7b
(/.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)) (-.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))) 3)) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 2)
45.5b
(/.f64 (+.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (*.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))) (*.f64 (/.f64 beta alpha) (+.f64 2 (/.f64 16 (*.f64 alpha alpha))))))) (-.f64 (*.f64 2 (pow.f64 (/.f64 beta alpha) 3)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
44.7b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (*.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)
Compiler

Compiled 3494 to 2210 computations (36.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)
0.1b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)) (-.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))) 3))
1.6b
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
3.0b
(-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4))

rewrite325.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
215×add-sqr-sqrt_binary64
189×*-un-lft-identity_binary64
164×times-frac_binary64
152×unpow-prod-down_binary64
114×cbrt-prod_binary64
Counts
4 → 238
Calls

4 calls:

31.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)) (-.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))) 3))
22.0ms
(-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4))
13.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
10.0ms
(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)
Compiler

Compiled 11597 to 7301 computations (37% saved)

series502.0ms (7.4%)

Error
0.0b
Counts
4 → 55
Calls

4 calls:

239.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)) (-.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))) 3))
106.0ms
(-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4))
54.0ms
(+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
51.0ms
(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)
Compiler

Compiled 8271 to 6090 computations (26.4% saved)

simplify395.0ms (5.9%)

Algorithm
egg-herbie
Rules
287×associate-/l*_binary64
240×sqr-pow_binary64
218×associate-*l/_binary64
175×associate-/r*_binary64
174×times-frac_binary64
Counts
293 → 240
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
069416099
1202615496
2472315415
3498315415
4489015415

prune144.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2400240
Fresh022
Picked011
Done011
Total2404244
Error
0.0b
Counts
244 → 4
Alt Table
StatusErrorProgram
17.8b
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
33.7b
(/.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 4)) (-.f64 -1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))) 3)) (+.f64 -1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 2)
45.5b
(/.f64 (+.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (*.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))) (*.f64 (/.f64 beta alpha) (+.f64 2 (/.f64 16 (*.f64 alpha alpha))))))) (-.f64 (*.f64 2 (pow.f64 (/.f64 beta alpha) 3)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
44.7b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (*.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (*.f64 6 (/.f64 beta (*.f64 alpha alpha))) (*.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)
Compiler

Compiled 6955 to 4413 computations (36.5% saved)

regimes659.0ms (9.8%)

Accuracy

Total 0.0b remaining (45.5%)

Threshold costs 0.0b (45.5%)

Compiler

Compiled 14088 to 9865 computations (30% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
18×+-commutative_binary64
13×*-commutative_binary64
12×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03389
14789
25889
37589
410189
511689
612789
713389
813589
913189

end1.0ms (0%)

Compiler

Compiled 62 to 37 computations (40.3% saved)

sample1.4s (21.2%)

Algorithm
intervals
Results
267.0ms5979×body128valid
169.0ms1060×body1024valid
157.0ms8000×pre128true
69.0ms576×body512valid
30.0ms299×body256valid
16.0ms86×body2048valid
Compiler

Compiled 259 to 165 computations (36.3% saved)

Profiling

Loading profile data...