Details

Time bar (total: 43.9s)

analyze163.0ms (0.4%)

Algorithm
1×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)

sample42.0ms (0.1%)

Algorithm
1×intervals
Results
12.0ms211×body128valid
6.0ms256×pre128true
4.0ms18×body1024valid
3.0ms16×body512valid
1.0ms9×body256valid
1.0ms2×body2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify187.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
23.1b
Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0%)

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))
1.9b
(+.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)
21.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite377.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
11.7b
Rules
54×times-frac_binary64_1448
47×*-un-lft-identity_binary64_1442
25×add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464
17×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
14×associate-/r/_binary64_1388
11×flip3-+_binary64_1445 flip-+_binary64_1416 distribute-lft-out_binary64_1393
10×associate-/l*_binary64_1387
9×associate-/l/_binary64_1389
7×div-exp_binary64_1493 cbrt-undiv_binary64_1476 div-inv_binary64_1439 associate-/r*_binary64_1386
5×add-log-exp_binary64_1481
4×frac-times_binary64_1452
3×pow1_binary64_1503 flip3--_binary64_1446 flip--_binary64_1417
2×prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-2neg_binary64_1453 clear-num_binary64_1441 associate-*l/_binary64_1385 associate-*r/_binary64_1384
1×sum-log_binary64_1533 +-commutative_binary64_1372
Counts
3 → 111
Calls

3 calls:

45.0ms
(+.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)
27.0ms
(/.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))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 5370 to 2710 computations (49.5% saved)

series4.2s (9.6%)

Error
0.6b
Counts
3 → 72
Calls

3 calls:

2.1s
(+.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)
1.5s
(/.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))
290.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 15544 to 12049 computations (22.5% saved)

simplify161.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0555012903

prune628.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1785183
Fresh000
Picked101
Done000
Total1795184
Error
0.0b
Counts
184 → 5
Compiler

Compiled 10667 to 6081 computations (43% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b
(/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b
(*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
1.9b
(+.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite390.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
48×*-un-lft-identity_binary64_1442
45×add-sqr-sqrt_binary64_1464
35×times-frac_binary64_1448
26×add-cube-cbrt_binary64_1477
21×associate-*r*_binary64_1382
20×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
8×flip3-+_binary64_1445 flip-+_binary64_1416
7×difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394 associate-/l/_binary64_1389 associate-/r*_binary64_1386
6×add-log-exp_binary64_1481 pow1_binary64_1503 div-exp_binary64_1493 cbrt-undiv_binary64_1476 associate-/r/_binary64_1388 associate-/l*_binary64_1387
4×distribute-lft-out_binary64_1393 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*l*_binary64_1383
3×div-inv_binary64_1439
2×unswap-sqr_binary64_1410 associate-*r/_binary64_1384 frac-2neg_binary64_1453 clear-num_binary64_1441
1×sum-log_binary64_1533 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 div-sub_binary64_1447 flip3--_binary64_1446 flip--_binary64_1417
Counts
4 → 129
Calls

4 calls:

33.0ms
(/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
32.0ms
(+.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
24.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
13.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 5642 to 2885 computations (48.9% saved)

series4.7s (10.7%)

Error
0.0b
Counts
4 → 98
Calls

4 calls:

2.1s
(+.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.4s
(/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
330.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
305.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
Compiler

Compiled 18664 to 14298 computations (23.4% saved)

simplify179.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0585713095

prune741.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2261227
Fresh134
Picked011
Done000
Total2275232
Error
0.0b
Counts
232 → 5
Compiler

Compiled 12204 to 7137 computations (41.5% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
1.9b
(+.f64 (log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))) 1)
2.1b
(log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))

rewrite391.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
59×*-un-lft-identity_binary64_1442
34×add-sqr-sqrt_binary64_1464
31×times-frac_binary64_1448
26×associate-*r*_binary64_1382
21×add-cube-cbrt_binary64_1477
18×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
17×distribute-lft-out_binary64_1393
13×log-pow_binary64_1531
11×exp-prod_binary64_1494
8×pow1_binary64_1503 flip3-+_binary64_1445 flip-+_binary64_1416
6×associate-/r/_binary64_1388 log-prod_binary64_1528
5×add-log-exp_binary64_1481 div-exp_binary64_1493 cbrt-undiv_binary64_1476 associate-/l/_binary64_1389 associate-/r*_binary64_1386
4×prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*l*_binary64_1383 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
3×div-inv_binary64_1439 associate-+l+_binary64_1375
2×unswap-sqr_binary64_1410 associate-*r/_binary64_1384
1×rem-log-exp_binary64_1483 sum-log_binary64_1533 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 frac-2neg_binary64_1453 clear-num_binary64_1441 associate-/l*_binary64_1387
Counts
4 → 123
Calls

4 calls:

29.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
28.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
24.0ms
(+.f64 (log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))) 1)
11.0ms
(log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))
Compiler

Compiled 5809 to 3507 computations (39.6% saved)

series9.8s (22.2%)

Error
0.0b
Counts
4 → 98
Calls

4 calls:

4.4s
(+.f64 (log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))) 1)
3.1s
(log.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))
1.3s
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
284.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
Compiler

Compiled 22790 to 17763 computations (22.1% saved)

simplify197.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0561715320

prune922.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2192221
Fresh123
Picked101
Done011
Total2215226
Error
0.0b
Counts
226 → 5
Compiler

Compiled 13425 to 8290 computations (38.2% saved)

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
1.9b
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))) (+.f64 1 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))))
2.2b
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
2.2b
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))

rewrite688.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
66×*-un-lft-identity_binary64_1442
38×add-sqr-sqrt_binary64_1464
33×log-pow_binary64_1531
31×times-frac_binary64_1448
26×associate-*r*_binary64_1382
25×add-cube-cbrt_binary64_1477
24×sqrt-pow1_binary64_1460
22×exp-prod_binary64_1494 distribute-lft-out_binary64_1393
18×log-prod_binary64_1528
15×pow1_binary64_1503
11×add-exp-log_binary64_1480
9×sqrt-prod_binary64_1458 add-cbrt-cube_binary64_1478
6×flip3-+_binary64_1445 associate-/r/_binary64_1388 flip-+_binary64_1416 add-log-exp_binary64_1481 associate-+l+_binary64_1375
4×associate-*l*_binary64_1383 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
3×div-inv_binary64_1439 sum-log_binary64_1533
2×pow1/2_binary64_1522 rem-log-exp_binary64_1483 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-times_binary64_1452 unswap-sqr_binary64_1410 associate-*l/_binary64_1385
1×associate-+r+_binary64_1374 +-commutative_binary64_1372 pow-prod-down_binary64_1513 div-exp_binary64_1493 cbrt-undiv_binary64_1476 associate-*r/_binary64_1384 *-commutative_binary64_1373
Counts
4 → 131
Calls

4 calls:

46.0ms
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))) (+.f64 1 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))))
28.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
12.0ms
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
12.0ms
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))
Compiler

Compiled 10552 to 6409 computations (39.3% saved)

series13.0s (29.5%)

Error
0.0b
Counts
4 → 98
Calls

4 calls:

4.7s
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))) (+.f64 1 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))))
3.6s
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
3.6s
(log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))))))
314.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
Compiler

Compiled 26406 to 19934 computations (24.5% saved)

simplify197.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0516417600

prune1.5s (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2290229
Fresh033
Picked011
Done011
Total2295234
Error
0.0b
Counts
234 → 5
Compiler

Compiled 20019 to 12242 computations (38.8% saved)

regimes1.5s (3.5%)

Accuracy

Total 1.4b remaining (94.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20310 to 14568 computations (28.3% saved)

bsearch6.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
062123
162123

end0.0ms (0%)

sample3.9s (8.9%)

Algorithm
1×intervals
Results
495.0ms6518×body128valid
245.0ms8000×pre128true
195.0ms646×body1024valid
108.0ms496×body512valid
42.0ms298×body256valid
15.0ms42×body2048valid
Compiler

Compiled 2946 to 2107 computations (28.5% saved)

Profiling

Loading profile data...