Details

Time bar (total: 12.2s)

analyze127.0ms (1%)

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)

sample36.0ms (0.3%)

Algorithm
intervals
Results
12.0ms205×body128valid
6.0ms27×body1024valid
6.0ms256×pre128true
2.0ms15×body512valid
1.0msbody2048valid
1.0msbody256valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify162.0ms (1.3%)

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
23.8b
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))
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)
21.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite91.0ms (0.7%)

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)))

series708.0ms (5.8%)

Counts
3 → 9
Calls

3 calls:

354.0ms
(+.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)
293.0ms
(/.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)))

simplify107.0ms (0.9%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049415261
149415261

prune237.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1137120
Fresh000
Picked101
Done000
Total1147121
Error
6.9b
Counts
121 → 7
Compiler

Compiled 5214 to 2727 computations (47.7% 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)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
3.2b
(*.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)

rewrite162.0ms (1.3%)

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:

48.0ms
(*.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)
20.0ms
(/.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)))

series860.0ms (7%)

Counts
4 → 12
Calls

4 calls:

350.0ms
(+.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)
295.0ms
(*.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)))

simplify165.0ms (1.3%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0501413438

prune791.0ms (6.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3007307
Fresh336
Picked101
Done000
Total30410314
Error
6.9b
Counts
314 → 10
Compiler

Compiled 14705 to 7765 computations (47.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
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))
3.2b
(*.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)

rewrite179.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
306×times-frac_binary64_1448
275×*-un-lft-identity_binary64_1442
196×add-sqr-sqrt_binary64_1464
133×add-cube-cbrt_binary64_1477
90×associate-*r*_binary64_1382
44×distribute-lft-out_binary64_1393
27×difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
22×associate-/r/_binary64_1388
21×associate-/l*_binary64_1387
18×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
15×flip3-+_binary64_1445 flip-+_binary64_1416
12×cbrt-prod_binary64_1473
11×div-inv_binary64_1439
cbrt-undiv_binary64_1476 add-log-exp_binary64_1481 pow1_binary64_1503 div-exp_binary64_1493
associate-/r*_binary64_1386 associate-*l*_binary64_1383
cbrt-unprod_binary64_1475 cube-prod_binary64_1470 prod-exp_binary64_1491 unpow-prod-down_binary64_1521 unswap-sqr_binary64_1410
cbrt-div_binary64_1474 frac-times_binary64_1452 cube-div_binary64_1471 div-sub_binary64_1447 associate-*l/_binary64_1385
associate-*r/_binary64_1384 cube-mult_binary64_1472 sum-log_binary64_1533 associate-/l/_binary64_1389 clear-num_binary64_1441 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 frac-2neg_binary64_1453 sqr-pow_binary64_1414 unpow3_binary64_1508 pow1/3_binary64_1524 rem-cbrt-cube_binary64_1466
Counts
4 → 278
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)))))
32.0ms
(+.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)
30.0ms
(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))
24.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.2s (9.5%)

Counts
4 → 12
Calls

4 calls:

356.0ms
(+.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)
347.0ms
(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))
301.0ms
(*.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)))))
154.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify145.0ms (1.2%)

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0509513897

prune745.0ms (6.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2846290
Fresh549
Picked101
Done000
Total29010300
Error
6.9b
Counts
300 → 10
Compiler

Compiled 15071 to 8391 computations (44.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(cbrt.f64 (pow.f64 (log.f64 (exp.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))
3.2b
(*.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)
4.2b
(log.f64 (exp.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)))

rewrite178.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
147×times-frac_binary64_1448
138×*-un-lft-identity_binary64_1442
103×add-sqr-sqrt_binary64_1464
90×associate-*r*_binary64_1382
70×add-cube-cbrt_binary64_1477
22×distribute-lft-out_binary64_1393
20×cbrt-prod_binary64_1473
13×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×log-pow_binary64_1531 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
10×associate-/r/_binary64_1388
exp-prod_binary64_1494 pow1_binary64_1503
flip3-+_binary64_1445 flip-+_binary64_1416
cube-prod_binary64_1470 unpow-prod-down_binary64_1521
add-log-exp_binary64_1481
div-inv_binary64_1439
log-prod_binary64_1528 associate-*l*_binary64_1383
cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475 prod-exp_binary64_1491 div-exp_binary64_1493 unswap-sqr_binary64_1410
frac-times_binary64_1452 associate-*l/_binary64_1385
associate-*r/_binary64_1384 cube-mult_binary64_1472 sum-log_binary64_1533 rem-log-exp_binary64_1483 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 sqr-pow_binary64_1414 unpow3_binary64_1508 pow1/3_binary64_1524 exp-sum_binary64_1488 rem-cbrt-cube_binary64_1466
Counts
4 → 173
Calls

4 calls:

48.0ms
(*.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)))))
31.0ms
(+.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)
31.0ms
(cbrt.f64 (pow.f64 (log.f64 (exp.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))
30.0ms
(log.f64 (exp.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)))

series1.8s (14.5%)

Counts
4 → 12
Calls

4 calls:

582.0ms
(cbrt.f64 (pow.f64 (log.f64 (exp.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))
572.0ms
(log.f64 (exp.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)))
332.0ms
(+.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)
290.0ms
(*.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)))))

simplify116.0ms (0.9%)

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
051067776

prune451.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1850185
Fresh099
Picked011
Done000
Total18510195
Error
6.9b
Counts
195 → 10
Compiler

Compiled 9197 to 5240 computations (43% saved)

regimes1.2s (9.9%)

Accuracy

Total 1.8b remaining (22.7%)

Threshold costs 0b (0%)

Compiler

Compiled 20444 to 13124 computations (35.8% saved)

bsearch5.0ms (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%)

sample2.8s (22.6%)

Algorithm
intervals
Results
377.0ms6452×body128valid
185.0ms8000×pre128true
154.0ms676×body1024valid
90.0ms514×body512valid
37.0ms312×body256valid
13.0ms46×body2048valid
Compiler

Compiled 2971 to 1905 computations (35.9% saved)

Profiling

Loading profile data...