Details

Time bar (total: 2.5min)

analyze4.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6
Compiler

Compiled 42 to 29 computations (31% saved)

sample32.0ms (0%)

Algorithm
1×intervals
Results
15.0ms256×body128valid
4.0ms256×pre128true
Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify327.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (231.0ms)

IterNodesCost
0502337

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
1.5b
Counts
2 → 2
Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
5.9b
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.0b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite410.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
77×*-un-lft-identity_binary64_1442
34×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478 distribute-lft-out_binary64_1393
24×flip3-+_binary64_1445 flip-+_binary64_1416
21×add-sqr-sqrt_binary64_1464 associate-*r*_binary64_1382
18×associate-/r/_binary64_1388
16×frac-times_binary64_1452
15×add-cube-cbrt_binary64_1477
14×times-frac_binary64_1448
13×pow1_binary64_1503
11×swap-sqr_binary64_1409
10×prod-exp_binary64_1491 div-exp_binary64_1493 cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475 associate-*l/_binary64_1385
9×associate-*l*_binary64_1383
8×associate-*r/_binary64_1384
7×associate-/l/_binary64_1389
6×associate-/r*_binary64_1386
5×associate-/l*_binary64_1387
4×add-log-exp_binary64_1481
3×div-inv_binary64_1439 unswap-sqr_binary64_1410
2×frac-2neg_binary64_1453 clear-num_binary64_1441 pow-prod-down_binary64_1513 *-commutative_binary64_1373
1×pow2_binary64_1523 pow-prod-up_binary64_1512 pow-plus_binary64_1505 pow-sqr_binary64_1415 distribute-rgt-in_binary64_1392 distribute-lft-in_binary64_1391
Counts
4 → 158
Calls

4 calls:

33.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
23.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
15.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.7s (1.8%)

Error
0.3b
Counts
4 → 84
Calls

4 calls:

1.1s
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
529.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
394.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
109.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
Compiler

Compiled 16632 to 13223 computations (20.5% saved)

simplify128.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0543714115

prune784.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2348242
Fresh101
Picked101
Done000
Total2368244
Error
0.0b
Counts
244 → 8
Compiler

Compiled 12917 to 8745 computations (32.3% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.0b
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
0.0b
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
0.1b
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite505.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
192×*-un-lft-identity_binary64_1442
89×times-frac_binary64_1448
82×distribute-lft-out_binary64_1393
60×add-sqr-sqrt_binary64_1464
48×add-cube-cbrt_binary64_1477
38×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
26×associate-*l*_binary64_1383 associate-*r*_binary64_1382
15×div-exp_binary64_1493 cbrt-undiv_binary64_1476 associate-/r*_binary64_1386
10×associate-/r/_binary64_1388
9×associate-/l*_binary64_1387
8×prod-exp_binary64_1491 cbrt-unprod_binary64_1475
7×associate-/l/_binary64_1389 flip3-+_binary64_1445 flip-+_binary64_1416
6×pow1_binary64_1503
5×div-inv_binary64_1439
4×add-log-exp_binary64_1481 unswap-sqr_binary64_1410
3×frac-2neg_binary64_1453 clear-num_binary64_1441
2×frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*r/_binary64_1384
1×pow-prod-down_binary64_1513 *-commutative_binary64_1373
Counts
4 → 202
Calls

4 calls:

35.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
26.0ms
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
10.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
9.0ms
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
Compiler

Compiled 7414 to 4981 computations (32.8% saved)

series2.4s (1.6%)

Error
0.0b
Counts
4 → 88
Calls

4 calls:

1.1s
(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
539.0ms
(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
171.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
165.0ms
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
Compiler

Compiled 16640 to 13028 computations (21.7% saved)

simplify138.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0549215120

prune944.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2873290
Fresh437
Picked011
Done000
Total2917298
Error
0.0b
Counts
298 → 7
Compiler

Compiled 14460 to 9868 computations (31.8% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))
0.0b
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
0.1b
(/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)))
0.2b
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))))

rewrite1.1min (45.7%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
15581×*-un-lft-identity_binary64_1442
12730×times-frac_binary64_1448
6938×distribute-lft-out_binary64_1393
3552×add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464
587×associate-/r/_binary64_1388
308×div-inv_binary64_1439
282×flip3-+_binary64_1445 flip-+_binary64_1416
171×associate-/r*_binary64_1386
39×associate-/l*_binary64_1387
34×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
20×div-exp_binary64_1493 cbrt-undiv_binary64_1476
7×associate-/l/_binary64_1389
4×pow1_binary64_1503 add-log-exp_binary64_1481 frac-2neg_binary64_1453 clear-num_binary64_1441
Counts
4 → 3963
Calls

4 calls:

126.0ms
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))))
21.0ms
(/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)))
10.0ms
(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))
9.0ms
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
Compiler

Compiled 204741 to 151273 computations (26.1% saved)

series2.0s (1.3%)

Error
0.0b
Counts
4 → 87
Calls

4 calls:

1.1s
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))))
202.0ms
(/.f64 (+.f64 (+.f64 beta 3) alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)))
177.0ms
(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))
159.0ms
(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
Compiler

Compiled 13917 to 10822 computations (22.2% saved)

simplify2.1s (1.4%)

Algorithm
1×egg-herbie
Counts
4050 → 4050
Iterations

Useful iterations: 0 (146.0ms)

IterNodesCost
05611280220

prune55.8s (37.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New404824050
Fresh145
Picked101
Done011
Total405074057
Error
0b
Counts
4057 → 7
Compiler

Compiled 194847 to 140053 computations (28.1% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))
0.1b
(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))))
0.5b
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))
0.6b
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))

rewrite6.5s (4.3%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
2156×*-un-lft-identity_binary64_1442
1592×times-frac_binary64_1448
917×distribute-lft-out_binary64_1393
679×add-sqr-sqrt_binary64_1464
569×add-cube-cbrt_binary64_1477
550×sqrt-prod_binary64_1458
214×associate-*l*_binary64_1383 associate-*r*_binary64_1382
78×associate-/r/_binary64_1388
56×associate-/l*_binary64_1387
52×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
40×flip3-+_binary64_1445 flip-+_binary64_1416
39×div-inv_binary64_1439
25×div-exp_binary64_1493 cbrt-undiv_binary64_1476 unswap-sqr_binary64_1410
21×associate-/r*_binary64_1386
9×prod-exp_binary64_1491 cbrt-unprod_binary64_1475
8×sqrt-div_binary64_1459
6×pow1_binary64_1503
4×add-log-exp_binary64_1481 associate-/l/_binary64_1389
3×frac-2neg_binary64_1453 clear-num_binary64_1441
1×pow-prod-down_binary64_1513 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*r/_binary64_1384 *-commutative_binary64_1373
Counts
4 → 1046
Calls

4 calls:

562.0ms
(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))))
22.0ms
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))
22.0ms
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))
9.0ms
(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))
Compiler

Compiled 54059 to 39554 computations (26.8% saved)

series2.4s (1.6%)

Error
0b
Counts
4 → 68
Calls

4 calls:

1.0s
(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha))))
370.0ms
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))
354.0ms
(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 (+.f64 beta 3) alpha)))
165.0ms
(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))
Compiler

Compiled 16786 to 13271 computations (20.9% saved)

simplify479.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1114 → 1114
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
0495358296
1495358296

prune3.7s (2.5%)

Profiling

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