Details

Time bar (total: 15.0s)

analyze127.0ms (0.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample35.0ms (0.2%)

Algorithm
intervals
Results
13.0ms220×body128valid
6.0ms256×pre128true
3.0ms20×body512valid
3.0ms12×body1024valid
0.0msbody256valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify58.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0506343

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 25.3b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.8b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
22.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite95.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64
47×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
17×add-exp-log_binary64 add-cbrt-cube_binary64
14×associate-/r/_binary64
11×flip3-+_binary64 distribute-lft-out_binary64 flip-+_binary64
10×associate-/l*_binary64
associate-/l/_binary64
associate-/r*_binary64 cbrt-undiv_binary64 div-inv_binary64 div-exp_binary64
add-log-exp_binary64
frac-times_binary64
pow1_binary64 flip3--_binary64 flip--_binary64
cbrt-unprod_binary64 associate-*r/_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 associate-*l/_binary64
+-commutative_binary64 sum-log_binary64
Counts
3 → 111
Calls

3 calls:

36.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
24.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
16.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (9.2%)

Counts
3 → 9
Calls

3 calls:

679.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
579.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
122.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify96.0ms (0.6%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049375261
149375261

prune242.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1128120
Fresh000
Picked101
Done000
Total1138121

Merged error: 4.9b

Counts
121 → 8
Compiler

Compiled 5283 to 2771 computations (47.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
2.5b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.5b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite163.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
321×times-frac_binary64
290×*-un-lft-identity_binary64
211×add-sqr-sqrt_binary64
140×add-cube-cbrt_binary64
90×associate-*r*_binary64
44×distribute-lft-out_binary64
31×difference-of-squares_binary64 distribute-lft-out--_binary64
26×associate-/l*_binary64
24×associate-/r/_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
15×flip3-+_binary64 flip-+_binary64
12×div-inv_binary64
associate-/r*_binary64 cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 pow1_binary64
associate-*l*_binary64
associate-/l/_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 div-sub_binary64 prod-exp_binary64
clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64
pow-prod-down_binary64 flip3--_binary64 associate-*r/_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 295
Calls

4 calls:

44.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
26.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (11.6%)

Counts
4 → 12
Calls

4 calls:

697.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
595.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
323.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
127.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify156.0ms (1%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0497113438
1497113438

prune693.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3025307
Fresh527
Picked101
Done000
Total3087315

Merged error: 4.9b

Counts
315 → 7
Compiler

Compiled 14557 to 7664 computations (47.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
3.3b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
4.2b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite278.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
378×times-frac_binary64
278×*-un-lft-identity_binary64
233×cbrt-prod_binary64
216×associate-*r*_binary64
214×add-sqr-sqrt_binary64
172×add-cube-cbrt_binary64
97×add-exp-log_binary64
55×add-cbrt-cube_binary64
45×cbrt-unprod_binary64 prod-exp_binary64
32×distribute-lft-out_binary64
30×cbrt-undiv_binary64 div-exp_binary64
21×difference-of-squares_binary64 distribute-lft-out--_binary64
16×associate-/r/_binary64
15×flip3-+_binary64 flip-+_binary64
pow1_binary64 frac-times_binary64 associate-*l/_binary64
div-inv_binary64
cbrt-div_binary64 add-log-exp_binary64
pow-prod-down_binary64 associate-*r/_binary64
pow1/3_binary64
associate-*l*_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 313
Calls

4 calls:

94.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
69.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
12.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.9s (12.9%)

Counts
4 → 12
Calls

4 calls:

722.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
618.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
294.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
293.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify255.0ms (1.7%)

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
0498127736
1498127736

prune1.5s (10.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3223325
Fresh066
Picked101
Done000
Total3239332

Merged error: 4.9b

Counts
332 → 9
Compiler

Compiled 27601 to 14185 computations (48.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
3.3b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
4.2b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite290.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
378×times-frac_binary64
278×*-un-lft-identity_binary64
233×cbrt-prod_binary64
216×associate-*r*_binary64
214×add-sqr-sqrt_binary64
172×add-cube-cbrt_binary64
97×add-exp-log_binary64
55×add-cbrt-cube_binary64
45×cbrt-unprod_binary64 prod-exp_binary64
32×distribute-lft-out_binary64
30×cbrt-undiv_binary64 div-exp_binary64
21×difference-of-squares_binary64 distribute-lft-out--_binary64
16×associate-/r/_binary64
15×flip3-+_binary64 flip-+_binary64
pow1_binary64 frac-times_binary64 associate-*l/_binary64
div-inv_binary64
cbrt-div_binary64 add-log-exp_binary64
pow-prod-down_binary64 associate-*r/_binary64
pow1/3_binary64
associate-*l*_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 313
Calls

4 calls:

100.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
74.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.9s (12.9%)

Counts
4 → 12
Calls

4 calls:

723.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
625.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
299.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
281.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify258.0ms (1.7%)

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0498127736
1498127736

prune1.6s (10.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3196325
Fresh448
Picked101
Done000
Total32410334

Merged error: 4.9b

Counts
334 → 10
Compiler

Compiled 27937 to 14788 computations (47.1% saved)

regimes205.0ms (1.4%)

Compiler

Compiled 3396 to 2032 computations (40.2% saved)

bsearch91.0ms (0.6%)

Steps
ItersRangePoint
7
9.36760786257702e+169
1.3253853089700093e+172
3.1228122934029902e+171
7
1.5697809024179216e+75
5.095824022338607e+76
1.800621932398946e+75
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
090460
190460

end0.0ms (0%)

sample1.7s (11.5%)

Algorithm
intervals
Results
388.0ms6507×body128valid
192.0ms8000×pre128true
152.0ms647×body1024valid
89.0ms528×body512valid
32.0ms280×body256valid
11.0ms38×body2048valid
Compiler

Compiled 1182 to 697 computations (41% saved)

Profiling

Loading profile data...