Details

Time bar (total: 1.7min)

analyze2.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 13 to 13 computations (0% saved)

sample43.0ms (0%)

Algorithm
1×intervals
Results
18.0ms72×body2048valid
9.0ms127×body128valid
5.0ms27×body1024valid
3.0ms22×body512valid
1.0ms8×body256valid
Compiler

Compiled 25 to 26 computations (-4% saved)

simplify97.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
04515
14515

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
16.6b
Counts
2 → 2
Compiler

Compiled 10 to 10 computations (0% saved)

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

2.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite30.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×*-un-lft-identity_binary64_1442
23×add-sqr-sqrt_binary64_1464
14×add-cube-cbrt_binary64_1477
12×sqrt-prod_binary64_1458
9×times-frac_binary64_1448
7×cancel-sign-sub-inv_binary64_1408
5×add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481 add-exp-log_binary64_1480
4×pow1_binary64_1503 difference-of-squares_binary64_1411
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387 distribute-lft-out_binary64_1393 distribute-lft-out--_binary64_1394
2×sqrt-div_binary64_1459
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 flip3--_binary64_1446 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/2_binary64_1522 div-exp_binary64_1493
Counts
3 → 68
Calls

6 calls:

11.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms
(/.f64 1/2 (hypot.f64 1 x))
7.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series144.0ms (0.1%)

Counts
3 → 9
Calls

3 calls:

61.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
54.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
28.0ms
(/.f64 1/2 (hypot.f64 1 x))
Compiler

Compiled 204 to 204 computations (0% saved)

simplify93.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
048281244
148281244

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

2.3b
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
2.3b
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

rewrite20.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442
12×add-cube-cbrt_binary64_1477
9×times-frac_binary64_1448
7×add-exp-log_binary64_1480 pow1_binary64_1503
5×add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481
4×cancel-sign-sub-inv_binary64_1408
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387
2×sqrt-pow1_binary64_1460 associate-*r/_binary64_1384 sqrt-div_binary64_1459 sqrt-prod_binary64_1458 difference-of-squares_binary64_1411 div-exp_binary64_1493
1×inv-pow_binary64_1527 cbrt-undiv_binary64_1476 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 1-exp_binary64_1486 flip3--_binary64_1446 pow-prod-down_binary64_1513 rec-exp_binary64_1492 pow-flip_binary64_1516 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/2_binary64_1522 distribute-lft-out--_binary64_1394
Counts
3 → 62
Calls

6 calls:

8.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
4.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
3.0ms
(/.f64 1 (hypot.f64 1 x))
0.0ms
(/.f64 1 (hypot.f64 1 x))
0.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))

series169.0ms (0.2%)

Counts
3 → 9
Calls

3 calls:

75.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
68.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
25.0ms
(/.f64 1 (hypot.f64 1 x))
Compiler

Compiled 228 to 228 computations (0% saved)

simplify107.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
048371052
148371052

prune562.0ms (0.5%)

Pruning

47 alts after pruning (45 fresh and 2 done)

PrunedKeptTotal
New10345148
Fresh000
Picked000
Done022
Total10347150
Error
16.1b
Counts
150 → 47
Compiler

Compiled 2237 to 2072 computations (7.4% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))

rewrite51.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
65×*-un-lft-identity_binary64_1442
33×distribute-lft-out_binary64_1393
30×add-sqr-sqrt_binary64_1464
24×times-frac_binary64_1448
17×add-cube-cbrt_binary64_1477
16×sqrt-prod_binary64_1458
8×add-log-exp_binary64_1481
6×associate-/r*_binary64_1386 add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
5×flip3-+_binary64_1445 flip-+_binary64_1416 pow1_binary64_1503
4×associate-/l*_binary64_1387
2×sum-log_binary64_1533 associate-/l/_binary64_1389 associate-/r/_binary64_1388 +-commutative_binary64_1372 sqrt-div_binary64_1459
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453 pow1/2_binary64_1522 div-exp_binary64_1493
Counts
4 → 92
Calls

8 calls:

21.0ms
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series312.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

155.0ms
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
62.0ms
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
52.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
43.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 492 to 468 computations (4.9% saved)

simplify78.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049652746
149652746

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

2.3b
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.3b
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite28.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×*-un-lft-identity_binary64_1442
15×add-sqr-sqrt_binary64_1464
12×add-cube-cbrt_binary64_1477
9×times-frac_binary64_1448
7×add-log-exp_binary64_1481
6×distribute-lft-out_binary64_1393 sqrt-prod_binary64_1458
5×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
4×pow1_binary64_1503
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387 distribute-rgt-neg-in_binary64_1400
2×sum-log_binary64_1533 sqrt-div_binary64_1459 flip3-+_binary64_1445 flip-+_binary64_1416
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 associate-+r-_binary64_1376 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 clear-num_binary64_1441 unsub-neg_binary64_1436 +-commutative_binary64_1372 neg-log_binary64_1535 frac-2neg_binary64_1453 pow1/2_binary64_1522 neg-sub0_binary64_1437 div-exp_binary64_1493
Counts
3 → 61
Calls

6 calls:

12.0ms
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series141.0ms (0.1%)

Counts
3 → 9
Calls

3 calls:

60.0ms
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
51.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
30.0ms
(/.f64 1/2 (hypot.f64 1 x))
Compiler

Compiled 216 to 216 computations (0% saved)

simplify74.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049341029
149341029

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

2.3b
(-.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.0b
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
2.3b
(-.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
30×*-un-lft-identity_binary64_1442
24×add-sqr-sqrt_binary64_1464
20×add-cube-cbrt_binary64_1477
17×log-pow_binary64_1531
14×exp-prod_binary64_1494
12×sqrt-prod_binary64_1458
11×cancel-sign-sub-inv_binary64_1408
9×times-frac_binary64_1448
8×pow1_binary64_1503
6×add-cbrt-cube_binary64_1478 log-prod_binary64_1528 add-exp-log_binary64_1480
5×add-log-exp_binary64_1481
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387 distribute-lft-out_binary64_1393 associate--r+_binary64_1378
2×sqrt-div_binary64_1459 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 rem-log-exp_binary64_1483 flip3--_binary64_1446 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/2_binary64_1522 div-exp_binary64_1493
Counts
4 → 91
Calls

8 calls:

14.0ms
(-.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
8.0ms
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(/.f64 1/2 (hypot.f64 1 x))

series384.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

158.0ms
(-.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
148.0ms
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
51.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
26.0ms
(/.f64 1/2 (hypot.f64 1 x))
Compiler

Compiled 324 to 324 computations (0% saved)

simplify79.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
048971551
148971551

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x)))))))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.1b
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.1b
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))
2.3b
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))))))

rewrite55.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
114×add-sqr-sqrt_binary64_1464
109×sqrt-prod_binary64_1458
78×times-frac_binary64_1448
68×*-un-lft-identity_binary64_1442
51×add-cube-cbrt_binary64_1477
31×pow1_binary64_1503
30×sqrt-pow1_binary64_1460
20×swap-sqr_binary64_1409
16×associate-*r*_binary64_1382 associate-*l*_binary64_1383 unswap-sqr_binary64_1410
12×rem-sqrt-square_binary64_1455
10×inv-pow_binary64_1527 pow-flip_binary64_1516 pow1/2_binary64_1522
9×pow-prod-up_binary64_1512
8×div-inv_binary64_1439
6×add-cbrt-cube_binary64_1478 sqrt-div_binary64_1459 add-log-exp_binary64_1481 add-exp-log_binary64_1480
5×pow-prod-down_binary64_1513 pow-sqr_binary64_1415
4×cancel-sign-sub-inv_binary64_1408
3×sqr-abs_binary64_1457
2×difference-of-squares_binary64_1411
1×pow2_binary64_1523 associate-*r/_binary64_1384 cbrt-unprod_binary64_1475 sub-neg_binary64_1435 pow-plus_binary64_1505 flip3--_binary64_1446 *-commutative_binary64_1373 sqrt-unprod_binary64_1462 flip--_binary64_1417 diff-log_binary64_1534 frac-times_binary64_1452 prod-exp_binary64_1491 rem-square-sqrt_binary64_1454 distribute-lft-out--_binary64_1394 associate-*l/_binary64_1385
Counts
4 → 181
Calls

8 calls:

19.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))
4.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
4.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))))))
3.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.0ms
(/.f64 1 (hypot.f64 1 x))

series186.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

76.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))))))
42.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
41.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
25.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (hypot.f64 1 x))))
Compiler

Compiled 390 to 378 computations (3.1% saved)

simplify84.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049152795
149152795

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
0.0b
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (hypot.f64 1 x))
0.0b
(sqrt.f64 (hypot.f64 1 x))
0.2b
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
0.2b
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
0.8b
(*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))))
2.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))))))

rewrite110.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
339×add-sqr-sqrt_binary64_1464
330×sqrt-prod_binary64_1458
312×times-frac_binary64_1448
183×*-un-lft-identity_binary64_1442
178×add-cube-cbrt_binary64_1477
68×swap-sqr_binary64_1409
40×associate-*r*_binary64_1382 associate-*l*_binary64_1383
25×unswap-sqr_binary64_1410
20×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×associate-/r*_binary64_1386 associate-/l*_binary64_1387
11×pow1_binary64_1503
6×cbrt-undiv_binary64_1476 cancel-sign-sub-inv_binary64_1408 div-inv_binary64_1439 add-log-exp_binary64_1481 sqrt-undiv_binary64_1463 div-exp_binary64_1493
4×cbrt-unprod_binary64_1475 prod-exp_binary64_1491 difference-of-squares_binary64_1411
2×clear-num_binary64_1441 frac-2neg_binary64_1453 distribute-lft-out--_binary64_1394
1×pow2_binary64_1523 associate-*r/_binary64_1384 sub-neg_binary64_1435 pow-plus_binary64_1505 flip3--_binary64_1446 pow-prod-down_binary64_1513 *-commutative_binary64_1373 pow-sqr_binary64_1415 sqrt-unprod_binary64_1462 flip--_binary64_1417 diff-log_binary64_1534 frac-times_binary64_1452 rem-square-sqrt_binary64_1454 pow-prod-up_binary64_1512 associate-*l/_binary64_1385
Counts
4 → 344
Calls

8 calls:

41.0ms
(*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))))
7.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))))))
6.0ms
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
6.0ms
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
0.0ms
(sqrt.f64 (hypot.f64 1 x))

series288.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

94.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))))))
67.0ms
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
65.0ms
(/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x)))
61.0ms
(*.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (hypot.f64 1 x))))
Compiler

Compiled 420 to 408 computations (2.9% saved)

simplify182.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
356 → 356
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049148686
149148686

prune12.6s (12.1%)

Pruning

188 alts after pruning (182 fresh and 6 done)

PrunedKeptTotal
New667159826
Fresh172340
Picked000
Done167
Total685188873
Error
16.1b
Counts
873 → 188
Compiler

Compiled 14851 to 13614 computations (8.3% saved)

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
0.0b
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.5b
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.5b
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
2.6b
(-.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite89.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
62×sqrt-div_binary64_1459
41×add-sqr-sqrt_binary64_1464
38×sqrt-prod_binary64_1458
37×*-un-lft-identity_binary64_1442
31×flip3-+_binary64_1445 flip-+_binary64_1416
28×associate-*r/_binary64_1384
21×pow1_binary64_1503
17×add-cube-cbrt_binary64_1477
16×frac-sub_binary64_1451
12×frac-times_binary64_1452
11×swap-sqr_binary64_1409
9×sqrt-pow1_binary64_1460 cube-prod_binary64_1470 pow1/2_binary64_1522 unpow-prod-down_binary64_1521
8×add-log-exp_binary64_1481 associate-*l/_binary64_1385
7×associate-*r*_binary64_1382 add-cbrt-cube_binary64_1478 associate-*l*_binary64_1383 add-exp-log_binary64_1480 distribute-lft-out_binary64_1393
5×pow-prod-up_binary64_1512
4×sub-div_binary64_1449 difference-of-squares_binary64_1411 unswap-sqr_binary64_1410
3×pow-unpow_binary64_1519 pow-prod-down_binary64_1513 pow-sqr_binary64_1415 pow-pow_binary64_1514
2×rem-sqrt-square_binary64_1455 times-frac_binary64_1448 flip3--_binary64_1446 flip--_binary64_1417 cube-div_binary64_1471 distribute-lft-out--_binary64_1394
1×pow2_binary64_1523 sqr-abs_binary64_1457 cube-mult_binary64_1472 cancel-sign-sub-inv_binary64_1408 cbrt-unprod_binary64_1475 sum-log_binary64_1533 pow-exp_binary64_1510 sub-neg_binary64_1435 pow-plus_binary64_1505 +-commutative_binary64_1372 *-commutative_binary64_1373 sqrt-unprod_binary64_1462 rem-cube-cbrt_binary64_1465 diff-log_binary64_1534 distribute-rgt-out--_binary64_1396 sqr-pow_binary64_1414 unpow3_binary64_1508 prod-exp_binary64_1491 rem-square-sqrt_binary64_1454 sqrt-pow2_binary64_1461 pow-to-exp_binary64_1511
Counts
4 → 148
Calls

8 calls:

21.0ms
(-.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
20.0ms
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

series310.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

108.0ms
(-.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
104.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
53.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
45.0ms
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 1200 to 1116 computations (7% saved)

simplify78.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
050984277

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

2.3b
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))
0.0b
(/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))
0.0b
(/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))
2.3b
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))))

rewrite57.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
75×times-frac_binary64_1448
58×*-un-lft-identity_binary64_1442
50×add-sqr-sqrt_binary64_1464
46×add-cube-cbrt_binary64_1477
14×add-exp-log_binary64_1480
13×associate-/r*_binary64_1386
10×sqrt-prod_binary64_1458
9×distribute-lft-out_binary64_1393
8×add-cbrt-cube_binary64_1478
7×div-inv_binary64_1439 add-log-exp_binary64_1481 div-exp_binary64_1493
5×pow1_binary64_1503
4×distribute-rgt-neg-in_binary64_1400
3×cbrt-undiv_binary64_1476 associate-/r/_binary64_1388 associate-/l*_binary64_1387
2×sum-log_binary64_1533 1-exp_binary64_1486 rec-exp_binary64_1492 sqrt-div_binary64_1459 flip3-+_binary64_1445 flip-+_binary64_1416
1×distribute-rgt-out_binary64_1395 sqrt-pow1_binary64_1460 inv-pow_binary64_1527 associate-+r-_binary64_1376 distribute-rgt1-in_binary64_1398 rem-sqrt-square_binary64_1455 clear-num_binary64_1441 unsub-neg_binary64_1436 +-commutative_binary64_1372 neg-log_binary64_1535 pow-flip_binary64_1516 frac-2neg_binary64_1453 pow1/2_binary64_1522 neg-sub0_binary64_1437
Counts
3 → 114
Calls

6 calls:

22.0ms
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))))
19.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))
6.0ms
(/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))
0.0ms
(/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))
0.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))

series146.0ms (0.1%)

Counts
3 → 9
Calls

3 calls:

63.0ms
(+.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))))
52.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))))
31.0ms
(/.f64 1 (/.f64 (hypot.f64 1 x) 1/2))
Compiler

Compiled 216 to 216 computations (0% saved)

simplify76.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
048842059
148842059

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)))
0.0b
(sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))
0.0b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
0.5b
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))

rewrite46.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64_1464
30×sqrt-prod_binary64_1458
27×*-un-lft-identity_binary64_1442
24×cbrt-prod_binary64_1473
18×cube-prod_binary64_1470 unpow-prod-down_binary64_1521
15×add-cube-cbrt_binary64_1477
10×difference-of-squares_binary64_1411
7×pow1_binary64_1503
6×sqrt-div_binary64_1459 add-log-exp_binary64_1481
5×add-cbrt-cube_binary64_1478 times-frac_binary64_1448 add-exp-log_binary64_1480 distribute-lft-out--_binary64_1394
4×cube-div_binary64_1471
3×flip3--_binary64_1446 pow-unpow_binary64_1519 flip--_binary64_1417 pow-pow_binary64_1514
2×sqrt-pow1_binary64_1460 cube-mult_binary64_1472 cbrt-div_binary64_1474 sqr-pow_binary64_1414 unpow3_binary64_1508 pow1/2_binary64_1522
1×rem-sqrt-square_binary64_1455 sum-log_binary64_1533 pow-exp_binary64_1510 +-commutative_binary64_1372 rem-cube-cbrt_binary64_1465 distribute-lft-out_binary64_1393 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/3_binary64_1524 sqrt-pow2_binary64_1461 pow-to-exp_binary64_1511 rem-cbrt-cube_binary64_1466
Counts
4 → 105
Calls

8 calls:

13.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
9.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
7.0ms
(sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)))

series252.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

104.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
53.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
52.0ms
(sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))
43.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 534 to 510 computations (4.5% saved)

simplify72.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
048682221
148682221

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.0b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.0b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.5b
(sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.3b
(-.f64 1 (log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))

rewrite37.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64_1464
21×*-un-lft-identity_binary64_1442
16×sqrt-prod_binary64_1458
13×add-cube-cbrt_binary64_1477
10×associate-*r*_binary64_1382 cbrt-prod_binary64_1473 pow1_binary64_1503
7×log-pow_binary64_1531 add-log-exp_binary64_1481
6×add-cbrt-cube_binary64_1478 log-prod_binary64_1528 cancel-sign-sub-inv_binary64_1408 add-exp-log_binary64_1480
4×cbrt-div_binary64_1474 sqrt-div_binary64_1459
3×associate-*l*_binary64_1383 associate--r+_binary64_1378 unswap-sqr_binary64_1410
2×sqrt-pow1_binary64_1460 associate-*r/_binary64_1384 rem-sqrt-square_binary64_1455 distribute-lft-out_binary64_1393 exp-prod_binary64_1494 flip3-+_binary64_1445 flip-+_binary64_1416 exp-to-pow_binary64_1504 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
1×cbrt-unprod_binary64_1475 sub-neg_binary64_1435 rem-log-exp_binary64_1483 flip3--_binary64_1446 pow-prod-down_binary64_1513 *-commutative_binary64_1373 flip--_binary64_1417 diff-log_binary64_1534 pow1/3_binary64_1524 pow1/2_binary64_1522 prod-exp_binary64_1491
Counts
4 → 88
Calls

8 calls:

13.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
7.0ms
(sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms
(-.f64 1 (log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))
2.0ms
(log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.0ms
(/.f64 1/2 (hypot.f64 1 x))

series1.1s (1%)

Counts
4 → 12
Calls

4 calls:

383.0ms
(-.f64 1 (log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))
365.0ms
(log.f64 (exp.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
185.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
153.0ms
(sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 654 to 630 computations (3.7% saved)

simplify81.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049123036
149123036

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.1b
(sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))))))))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.2b
(cbrt.f64 (hypot.f64 1 x))
0.2b
(cbrt.f64 (hypot.f64 1 x))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))
2.3b
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))))))

rewrite33.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442
16×associate-*l*_binary64_1383
15×add-cube-cbrt_binary64_1477
14×sqrt-prod_binary64_1458
9×add-cbrt-cube_binary64_1478 times-frac_binary64_1448 add-exp-log_binary64_1480 pow1_binary64_1503
6×cbrt-prod_binary64_1473 add-log-exp_binary64_1481
4×cancel-sign-sub-inv_binary64_1408 sqrt-div_binary64_1459
3×associate-*r/_binary64_1384 cbrt-unprod_binary64_1475 pow-prod-down_binary64_1513 prod-exp_binary64_1491
2×pow1/3_binary64_1524 difference-of-squares_binary64_1411
1×associate-*r*_binary64_1382 div-inv_binary64_1439 sub-neg_binary64_1435 flip3--_binary64_1446 *-commutative_binary64_1373 flip--_binary64_1417 diff-log_binary64_1534 frac-times_binary64_1452 distribute-lft-out--_binary64_1394 associate-*l/_binary64_1385
Counts
4 → 74
Calls

8 calls:

18.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))
4.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))))))
1.0ms
(cbrt.f64 (hypot.f64 1 x))
1.0ms
(cbrt.f64 (hypot.f64 1 x))
0.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))))))))

series617.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

286.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))))))
179.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 (hypot.f64 1 x))))))
78.0ms
(cbrt.f64 (hypot.f64 1 x))
73.0ms
(cbrt.f64 (hypot.f64 1 x))
Compiler

Compiled 690 to 654 computations (5.2% saved)

simplify55.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
051522978

prune21.4s (20.4%)

Pruning

333 alts after pruning (322 fresh and 11 done)

PrunedKeptTotal
New425161586
Fresh16161177
Picked000
Done01111
Total441333774
Error
15.8b
Counts
774 → 333
Compiler

Compiled 24826 to 22783 computations (8.2% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
0.0b
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))) (+.f64 (*.f64 1 1) (-.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.5b
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)
0.5b
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
2.6b
(-.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite51.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64_1464
21×*-un-lft-identity_binary64_1442
16×sqrt-prod_binary64_1458 unpow-prod-down_binary64_1521
12×add-cube-cbrt_binary64_1477
9×cube-prod_binary64_1470
8×add-log-exp_binary64_1481 pow1_binary64_1503
6×pow-unpow_binary64_1519 add-exp-log_binary64_1480 pow-pow_binary64_1514
5×add-cbrt-cube_binary64_1478
4×difference-of-squares_binary64_1411
3×distribute-lft-out--_binary64_1394
2×sqrt-pow1_binary64_1460 pow-exp_binary64_1510 unpow2_binary64_1507 times-frac_binary64_1448 flip3--_binary64_1446 sqrt-div_binary64_1459 distribute-lft-out_binary64_1393 flip--_binary64_1417 sqr-pow_binary64_1414 pow1/2_binary64_1522 cube-div_binary64_1471 sqrt-pow2_binary64_1461 pow-to-exp_binary64_1511
1×cube-mult_binary64_1472 cancel-sign-sub-inv_binary64_1408 sum-log_binary64_1533 sub-neg_binary64_1435 +-commutative_binary64_1372 rem-cube-cbrt_binary64_1465 diff-log_binary64_1534 distribute-rgt-out--_binary64_1396 unpow3_binary64_1508 flip3-+_binary64_1445 flip-+_binary64_1416
Counts
4 → 91
Calls

8 calls:

12.0ms
(-.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
8.0ms
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))) (+.f64 (*.f64 1 1) (-.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

series345.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

107.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
103.0ms
(-.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
79.0ms
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)
56.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 1116 to 1044 computations (6.5% saved)

simplify84.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
050231907

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

2.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x)))))
2.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x))))))

rewrite21.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64_1464
19×*-un-lft-identity_binary64_1442
14×add-cube-cbrt_binary64_1477
9×times-frac_binary64_1448 sqrt-prod_binary64_1458
6×cancel-sign-sub-inv_binary64_1408
5×add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481 add-exp-log_binary64_1480
4×pow1_binary64_1503 difference-of-squares_binary64_1411
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387
2×sqrt-div_binary64_1459 distribute-lft-out--_binary64_1394
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 flip3--_binary64_1446 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/2_binary64_1522 div-exp_binary64_1493
Counts
3 → 65
Calls

6 calls:

10.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(/.f64 1/2 (hypot.f64 1 x))
0.0ms
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x)))))

series150.0ms (0.1%)

Counts
3 → 9
Calls

3 calls:

64.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x))))))
54.0ms
(sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 1) (/.f64 1/2 (hypot.f64 1 x)))))
32.0ms
(/.f64 1/2 (hypot.f64 1 x))
Compiler

Compiled 228 to 228 computations (0% saved)

simplify72.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049341202
149341202

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3))))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(/.f64 -1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3)))
0.0b
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))
0.0b
(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3))
0.5b
(pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3)
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))

rewrite54.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
50×log-pow_binary64_1531
46×add-sqr-sqrt_binary64_1464
45×exp-prod_binary64_1494
33×*-un-lft-identity_binary64_1442
32×cbrt-prod_binary64_1473
30×sqrt-prod_binary64_1458
26×cube-prod_binary64_1470 unpow-prod-down_binary64_1521
21×add-cube-cbrt_binary64_1477
10×pow1_binary64_1503 difference-of-squares_binary64_1411
6×add-log-exp_binary64_1481
5×add-cbrt-cube_binary64_1478 times-frac_binary64_1448 add-exp-log_binary64_1480 distribute-lft-out--_binary64_1394
3×log-prod_binary64_1528 pow-unpow_binary64_1519
2×cube-mult_binary64_1472 sqr-pow_binary64_1414 unpow3_binary64_1508
1×sum-log_binary64_1533 pow-exp_binary64_1510 rem-log-exp_binary64_1483 +-commutative_binary64_1372 rem-cube-cbrt_binary64_1465 distribute-lft-out_binary64_1393 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/3_binary64_1524 pow-to-exp_binary64_1511 rem-cbrt-cube_binary64_1466 pow-pow_binary64_1514
Counts
4 → 117
Calls

8 calls:

13.0ms
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))
11.0ms
(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3))
11.0ms
(pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3)
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(+.f64 1 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3)))

series541.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

211.0ms
(pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3)
143.0ms
(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))) 3))
140.0ms
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))
47.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 582 to 558 computations (4.1% saved)

simplify93.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
048942364
148942364

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x))))))))
0.0b
(sqrt.f64 (hypot.f64 1 x))
0.0b
(sqrt.f64 (hypot.f64 1 x))
0.0b
(/.f64 1 (hypot.f64 1 x))
0.1b
(/.f64 1 (sqrt.f64 (hypot.f64 1 x)))
0.2b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x)))))
2.3b
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))))))

rewrite100.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
180×sqrt-prod_binary64_1458
134×add-sqr-sqrt_binary64_1464
110×times-frac_binary64_1448
86×*-un-lft-identity_binary64_1442
68×associate-*r*_binary64_1382 add-cube-cbrt_binary64_1477
24×pow1_binary64_1503 unswap-sqr_binary64_1410
20×sqrt-pow1_binary64_1460
17×associate-*l*_binary64_1383
16×sqrt-div_binary64_1459
15×add-exp-log_binary64_1480
13×add-cbrt-cube_binary64_1478
12×pow-prod-down_binary64_1513
11×pow-flip_binary64_1516
8×pow1/2_binary64_1522
6×associate-/r*_binary64_1386 add-log-exp_binary64_1481 frac-times_binary64_1452 associate-*l/_binary64_1385
5×inv-pow_binary64_1527
4×associate-*r/_binary64_1384 cancel-sign-sub-inv_binary64_1408 cbrt-unprod_binary64_1475 div-inv_binary64_1439 prod-exp_binary64_1491 pow-prod-up_binary64_1512
3×associate-/l*_binary64_1387 sqrt-unprod_binary64_1462
2×*-commutative_binary64_1373 difference-of-squares_binary64_1411 div-exp_binary64_1493
1×cbrt-undiv_binary64_1476 sub-neg_binary64_1435 clear-num_binary64_1441 1-exp_binary64_1486 flip3--_binary64_1446 rec-exp_binary64_1492 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 pow3_binary64_1525 distribute-lft-out--_binary64_1394
Counts
4 → 220
Calls

8 calls:

29.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))
25.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x)))))
5.0ms
(/.f64 1 (sqrt.f64 (hypot.f64 1 x)))
4.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))))))
0.0ms
(/.f64 1 (hypot.f64 1 x))

series304.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

155.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x)))))
74.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))))))
46.0ms
(/.f64 1 (sqrt.f64 (hypot.f64 1 x)))
29.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 1 x)))))
Compiler

Compiled 480 to 462 computations (3.8% saved)

simplify144.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
048765892
148765892

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))
0.0b
(*.f64 (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3))) (+.f64 (*.f64 1 1) (/.f64 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1))))))
0.0b
(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))
0.5b
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
0.5b
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
1.8b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
2.3b
(-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))

rewrite96.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
81×add-sqr-sqrt_binary64_1464
73×*-un-lft-identity_binary64_1442
58×cube-prod_binary64_1470 unpow-prod-down_binary64_1521
44×sqrt-prod_binary64_1458
28×difference-of-squares_binary64_1411
20×cancel-sign-sub-inv_binary64_1408
19×add-cube-cbrt_binary64_1477
14×distribute-rgt-out--_binary64_1396
13×distribute-lft-out_binary64_1393 sqr-pow_binary64_1414
12×cube-div_binary64_1471
11×distribute-lft-out--_binary64_1394
8×sqrt-div_binary64_1459 add-log-exp_binary64_1481 pow1_binary64_1503
6×add-cbrt-cube_binary64_1478 pow-unpow_binary64_1519 add-exp-log_binary64_1480 flip3-+_binary64_1445 flip-+_binary64_1416 pow-pow_binary64_1514
4×frac-sub_binary64_1451
3×cube-mult_binary64_1472 unpow3_binary64_1508
2×sqrt-pow1_binary64_1460 pow-exp_binary64_1510 times-frac_binary64_1448 flip3--_binary64_1446 rem-cube-cbrt_binary64_1465 flip--_binary64_1417 pow1/2_binary64_1522 sqrt-pow2_binary64_1461 pow-to-exp_binary64_1511
1×difference-cubes_binary64_1444 sum-log_binary64_1533 sub-neg_binary64_1435 +-commutative_binary64_1372 diff-log_binary64_1534
Counts
4 → 171
Calls

8 calls:

38.0ms
(-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))
9.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
9.0ms
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
6.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))

series615.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

341.0ms
(-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))
109.0ms
(pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)
106.0ms
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
59.0ms
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 1896 to 1740 computations (8.2% saved)

simplify83.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
060225312

prune31.0s (29.6%)

Pruning

455 alts after pruning (440 fresh and 15 done)

PrunedKeptTotal
New573148721
Fresh25292317
Picked000
Done11516
Total5994551054
Error
15.8b
Counts
1054 → 455
Compiler

Compiled 16492 to 14940 computations (9.4% saved)

simplify853.0ms (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0534456027

regimes16.3s (15.6%)

Compiler

Compiled 224329 to 208855 computations (6.9% saved)

bsearch0.0ms (0%)

regimes5.4s (5.2%)

Compiler

Compiled 64206 to 61127 computations (4.8% saved)

bsearch0.0ms (0%)

regimes4.1s (3.9%)

Compiler

Compiled 51454 to 49183 computations (4.4% saved)

bsearch0.0ms (0%)

regimes568.0ms (0.5%)

Compiler

Compiled 5499 to 5458 computations (0.7% saved)

bsearch0.0ms (0%)

regimes449.0ms (0.4%)

Compiler

Compiled 4050 to 4086 computations (-0.9% saved)

bsearch0.0ms (0%)

regimes20.0ms (0%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch84.0ms (0.1%)

Steps
ItersRangePoint
9
1.0399040809532385e-82
1.0146283471968457e-73
3.009781794805557e-77
10
-3.379184825699637e-63
-1.9744685801392275e-81
-2.990867059748371e-77
Compiler

Compiled 145 to 137 computations (5.5% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
069216
169216

end0.0ms (0%)

sample2.4s (2.3%)

Algorithm
1×intervals
Results
554.0ms2132×body2048valid
193.0ms1008×body1024valid
183.0ms4113×body128valid
65.0ms485×body512valid
22.0ms262×body256valid
Compiler

Compiled 32152 to 29930 computations (6.9% saved)

Profiling

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