Details

Time bar (total: 14.2s)

analyze280.0ms (2%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04894172
14894172
033
133
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)

sample39.0ms (0.3%)

Algorithm
intervals
Results
12.0ms205×body128valid
6.0ms18×body1024valid
6.0ms256×pre128true
3.0ms17×body512valid
2.0ms15×body256valid
0.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify75.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
22.2b
Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (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))
2.0b
(+.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)
17.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite91.0ms (0.6%)

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

3 calls:

38.0ms
(+.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)
22.0ms
(/.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)))

series711.0ms (5%)

Counts
3 → 9
Calls

3 calls:

351.0ms
(+.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)
298.0ms
(/.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))
61.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify101.0ms (0.7%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049415261
149415261

prune236.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1146120
Fresh000
Picked101
Done000
Total1156121
Error
5.3b
Counts
121 → 6
Compiler

Compiled 5229 to 2731 computations (47.8% saved)

localize13.0ms (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))))
1.1b
(*.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)))))
4.2b
(+.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_1448
290×*-un-lft-identity_binary64_1442
211×add-sqr-sqrt_binary64_1464
140×add-cube-cbrt_binary64_1477
90×associate-*r*_binary64_1382
44×distribute-lft-out_binary64_1393
31×difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
26×associate-/l*_binary64_1387
24×associate-/r/_binary64_1388
20×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
15×flip3-+_binary64_1445 flip-+_binary64_1416
12×div-inv_binary64_1439
cbrt-undiv_binary64_1476 associate-/r*_binary64_1386 div-exp_binary64_1493
add-log-exp_binary64_1481 pow1_binary64_1503
associate-*l*_binary64_1383
cbrt-unprod_binary64_1475 associate-/l/_binary64_1389 prod-exp_binary64_1491 div-sub_binary64_1447 unswap-sqr_binary64_1410
clear-num_binary64_1441 frac-2neg_binary64_1453 frac-times_binary64_1452 associate-*l/_binary64_1385
associate-*r/_binary64_1384 sum-log_binary64_1533 flip3--_binary64_1446 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 flip--_binary64_1417
Counts
4 → 295
Calls

4 calls:

46.0ms
(*.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)))))
28.0ms
(+.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)
21.0ms
(/.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)))

series862.0ms (6.1%)

Counts
4 → 12
Calls

4 calls:

354.0ms
(+.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)
293.0ms
(*.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)))))
158.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
57.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify155.0ms (1.1%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0501413438

prune757.0ms (5.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3034307
Fresh235
Picked101
Done000
Total3067313
Error
5.3b
Counts
313 → 7
Compiler

Compiled 14563 to 7677 computations (47.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (+.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) 3)
0.1b
(cbrt.f64 (pow.f64 (+.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) 3))
1.1b
(*.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)))))
4.2b
(+.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)

rewrite172.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
147×times-frac_binary64_1448
137×*-un-lft-identity_binary64_1442
102×add-sqr-sqrt_binary64_1464
90×associate-*r*_binary64_1382
69×add-cube-cbrt_binary64_1477
22×distribute-lft-out_binary64_1393
14×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×cbrt-prod_binary64_1473 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
10×associate-/r/_binary64_1388 flip3-+_binary64_1445 flip-+_binary64_1416
pow1_binary64_1503
cube-prod_binary64_1470 add-log-exp_binary64_1481 unpow-prod-down_binary64_1521
div-inv_binary64_1439
associate-*l*_binary64_1383 cube-div_binary64_1471
cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475 pow-unpow_binary64_1519 prod-exp_binary64_1491 div-exp_binary64_1493 unswap-sqr_binary64_1410
cube-mult_binary64_1472 cbrt-div_binary64_1474 frac-times_binary64_1452 sqr-pow_binary64_1414 unpow3_binary64_1508 associate-*l/_binary64_1385
associate-*r/_binary64_1384 sum-log_binary64_1533 pow-exp_binary64_1510 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 rem-cube-cbrt_binary64_1465 pow1/3_binary64_1524 pow-to-exp_binary64_1511 rem-cbrt-cube_binary64_1466 pow-pow_binary64_1514
Counts
4 → 176
Calls

4 calls:

46.0ms
(*.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)))))
35.0ms
(pow.f64 (+.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) 3)
31.0ms
(cbrt.f64 (pow.f64 (+.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) 3))
29.0ms
(+.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)

series2.2s (15.8%)

Counts
4 → 12
Calls

4 calls:

1.1s
(pow.f64 (+.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) 3)
541.0ms
(+.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)
339.0ms
(cbrt.f64 (pow.f64 (+.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) 3))
284.0ms
(*.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)))))

simplify121.0ms (0.9%)

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050958304

prune419.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1826188
Fresh246
Picked101
Done000
Total18510195
Error
5.3b
Counts
195 → 10
Compiler

Compiled 9770 to 5461 computations (44.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.7b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.2b
(*.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))))))
5.9b
(+.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)

rewrite277.0ms (2%)

Algorithm
rewrite-expression-head
Rules
378×times-frac_binary64_1448
278×*-un-lft-identity_binary64_1442
233×cbrt-prod_binary64_1473
216×associate-*r*_binary64_1382
214×add-sqr-sqrt_binary64_1464
172×add-cube-cbrt_binary64_1477
97×add-exp-log_binary64_1480
55×add-cbrt-cube_binary64_1478
45×cbrt-unprod_binary64_1475 prod-exp_binary64_1491
32×distribute-lft-out_binary64_1393
30×cbrt-undiv_binary64_1476 div-exp_binary64_1493
21×difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
16×associate-/r/_binary64_1388
15×flip3-+_binary64_1445 flip-+_binary64_1416
frac-times_binary64_1452 pow1_binary64_1503 associate-*l/_binary64_1385
div-inv_binary64_1439
cbrt-div_binary64_1474 add-log-exp_binary64_1481
associate-*r/_binary64_1384 pow-prod-down_binary64_1513
pow1/3_binary64_1524
sum-log_binary64_1533 +-commutative_binary64_1372 associate-*l*_binary64_1383 *-commutative_binary64_1373
Counts
4 → 313
Calls

4 calls:

97.0ms
(*.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)
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))))

series980.0ms (6.9%)

Counts
4 → 12
Calls

4 calls:

364.0ms
(+.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)
299.0ms
(*.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))))))
159.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
157.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify246.0ms (1.7%)

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0499225817
1499225817

prune1.5s (10.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3232325
Fresh279
Picked101
Done000
Total3269335
Error
5.3b
Counts
335 → 9
Compiler

Compiled 26714 to 13971 computations (47.7% saved)

regimes1.4s (10%)

Accuracy

Total 1.5b remaining (21%)

Threshold costs 0b (0%)

Compiler

Compiled 26583 to 17121 computations (35.6% saved)

bsearch7.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067110
167110

end0.0ms (0%)

sample3.3s (23.2%)

Algorithm
intervals
Results
376.0ms6490×body128valid
195.0ms8000×pre128true
149.0ms672×body1024valid
93.0ms508×body512valid
30.0ms270×body256valid
17.0ms60×body2048valid
Compiler

Compiled 3848 to 2476 computations (35.7% saved)

Profiling

Loading profile data...