Details

Time bar (total: 35.1s)

analyze282.0ms (0.8%)

Algorithm
1×search
2×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)

sample40.0ms (0.1%)

Algorithm
1×intervals
Results
12.0ms211×body128valid
6.0ms256×pre128true
5.0ms23×body1024valid
1.0ms12×body256valid
1.0ms9×body512valid
0.0ms1×body2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify74.0ms (0.2%)

Algorithm
1×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
24.4b
Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)
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))
2.5b
(+.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)
22.7b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite355.0ms (1%)

Algorithm
1×rewrite-expression-head
Error
10.7b
Rules
54×times-frac_binary64_1448
50×*-un-lft-identity_binary64_1442
26×add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464
18×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
15×add-log-exp_binary64_1481
14×associate-/r/_binary64_1388
12×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 sum-log_binary64_1533
4×pow1_binary64_1503 frac-times_binary64_1452
3×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 +-commutative_binary64_1372
1×associate-+l+_binary64_1375
Counts
4 → 126
Calls

4 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)
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)))
9.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)
Compiler

Compiled 5937 to 3013 computations (49.3% saved)

series3.4s (9.7%)

Error
0.5b
Counts
4 → 86
Calls

4 calls:

1.6s
(+.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)
1.1s
(/.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))
253.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
112.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)
Compiler

Compiled 15451 to 11776 computations (23.8% saved)

simplify112.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0517212314

prune562.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2075212
Fresh000
Picked101
Done000
Total2085213
Error
0.1b
Counts
213 → 5
Compiler

Compiled 11037 to 6022 computations (45.4% saved)

localize17.0ms (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 beta alpha) (/.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))
2.5b
(+.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)

rewrite316.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.1b
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×associate-/l/_binary64_1389 associate-/r*_binary64_1386 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
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×frac-2neg_binary64_1453 clear-num_binary64_1441 associate-*r/_binary64_1384 unswap-sqr_binary64_1410
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:

27.0ms
(+.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 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
21.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 5642 to 2885 computations (48.9% saved)

series3.6s (10.1%)

Error
0.1b
Counts
4 → 90
Calls

4 calls:

1.6s
(+.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)
1.1s
(/.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))
250.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
246.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 16912 to 12932 computations (23.5% saved)

simplify110.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0513211677

prune600.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2181219
Fresh044
Picked011
Done000
Total2186224
Error
0.1b
Counts
224 → 6
Compiler

Compiled 11272 to 6387 computations (43.3% saved)

localize19.0ms (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))))
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))))
2.5b
(+.f64 1 (/.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)))))
2.5b
(log.f64 (exp.f64 (+.f64 1 (/.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)))))))

rewrite335.0ms (1%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
53×*-un-lft-identity_binary64_1442
32×add-sqr-sqrt_binary64_1464
26×times-frac_binary64_1448 associate-*r*_binary64_1382
19×add-cube-cbrt_binary64_1477
18×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
14×distribute-lft-out_binary64_1393
7×pow1_binary64_1503 flip3-+_binary64_1445 flip-+_binary64_1416
6×add-log-exp_binary64_1481
5×log-pow_binary64_1531 div-exp_binary64_1493 cbrt-undiv_binary64_1476 associate-/l/_binary64_1389 associate-/r*_binary64_1386
4×exp-prod_binary64_1494 log-prod_binary64_1528 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-/r/_binary64_1388 associate-*l*_binary64_1383 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
2×div-inv_binary64_1439 associate-*r/_binary64_1384 unswap-sqr_binary64_1410
1×exp-sum_binary64_1488 rem-log-exp_binary64_1483 sum-log_binary64_1533 +-commutative_binary64_1372 frac-2neg_binary64_1453 clear-num_binary64_1441 associate-/l*_binary64_1387 pow-prod-down_binary64_1513 *-commutative_binary64_1373
Counts
4 → 113
Calls

4 calls:

25.0ms
(/.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))))
21.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
15.0ms
(log.f64 (exp.f64 (+.f64 1 (/.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)))))))
14.0ms
(+.f64 1 (/.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 5317 to 3195 computations (39.9% saved)

series6.0s (17.1%)

Error
0.1b
Counts
4 → 91
Calls

4 calls:

2.8s
(log.f64 (exp.f64 (+.f64 1 (/.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)))))))
1.4s
(+.f64 1 (/.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)))))
1.1s
(/.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))))
260.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (*.f64 2 i) beta))))
Compiler

Compiled 20261 to 15812 computations (22% saved)

simplify148.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0498213799
1498213799

prune773.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2031204
Fresh044
Picked101
Done011
Total2046210
Error
0.1b
Counts
210 → 6
Compiler

Compiled 12225 to 7304 computations (40.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(+.f64 1 (/.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))))
2.5b
(+.f64 1 (/.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))))
2.5b
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))
2.5b
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))

rewrite328.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
18×*-un-lft-identity_binary64_1442
14×log-pow_binary64_1531 log-prod_binary64_1528
10×sqrt-pow1_binary64_1460 add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464
8×pow1_binary64_1503 exp-prod_binary64_1494 sqrt-prod_binary64_1458 add-log-exp_binary64_1481
6×add-exp-log_binary64_1480
4×distribute-lft-out_binary64_1393 add-cbrt-cube_binary64_1478
2×pow1/2_binary64_1522 exp-sum_binary64_1488 rem-log-exp_binary64_1483 sum-log_binary64_1533 flip3-+_binary64_1445 flip-+_binary64_1416 +-commutative_binary64_1372
Counts
4 → 68
Calls

4 calls:

17.0ms
(+.f64 1 (/.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))))
16.0ms
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))
15.0ms
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))
13.0ms
(+.f64 1 (/.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 5840 to 3637 computations (37.7% saved)

series12.6s (35.9%)

Error
0.1b
Counts
4 → 94
Calls

4 calls:

4.4s
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))
4.3s
(log.f64 (sqrt.f64 (exp.f64 (+.f64 1 (/.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)))))))
1.4s
(+.f64 1 (/.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))))
1.4s
(+.f64 1 (/.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 30592 to 22934 computations (25% saved)

simplify143.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0512417014

prune1.1s (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1620162
Fresh044
Picked011
Done011
Total1626168
Error
0.1b
Counts
168 → 6
Compiler

Compiled 17522 to 10570 computations (39.7% saved)

regimes1.2s (3.4%)

Accuracy

Total 1.2b remaining (94.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20140 to 13688 computations (32% saved)

bsearch5.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0272185
1272185

end0.0ms (0%)

sample2.9s (8.4%)

Algorithm
1×intervals
Results
381.0ms6567×body128valid
187.0ms8000×pre128true
154.0ms649×body1024valid
83.0ms462×body512valid
30.0ms267×body256valid
16.0ms55×body2048valid
Compiler

Compiled 2913 to 1966 computations (32.5% saved)

Profiling

Loading profile data...