Details

Time bar (total: 22.7s)

analyze4.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 9 to 5 computations (44.4% saved)

sample15.0ms (0.1%)

Algorithm
1×intervals
Results
6.0ms256×body128valid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify104.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01511
11511

prune4.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New033
Fresh033
Picked000
Done000
Total066
Error
29.9b
Counts
6 → 4
Compiler

Compiled 8 to 6 computations (25% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

29.4b
(sqrt.f64 (*.f64 x (+.f64 x x)))
29.4b
(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite6.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
4×pow1_binary64_480
2×sqrt-div_binary64_436 associate-*r/_binary64_361 sqrt-pow1_binary64_437
1×flip3-+_binary64_422 *-un-lft-identity_binary64_419 pow-prod-down_binary64_490 add-log-exp_binary64_458 add-cube-cbrt_binary64_454 pow1/2_binary64_499 add-sqr-sqrt_binary64_441 flip-+_binary64_393 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 sqrt-prod_binary64_435
Counts
1 → 13
Calls

2 calls:

5.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
0.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 28 to 28 computations (0% saved)

simplify72.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
05009140

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

29.4b
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
0.0b
(+.f64 (*.f64 x x) (*.f64 x x))
0.0b
(+.f64 (*.f64 x x) (*.f64 x x))
29.4b
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×sqrt-prod_binary64_435
4×add-log-exp_binary64_458 add-sqr-sqrt_binary64_441
3×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 pow1_binary64_480
2×flip3-+_binary64_422 sqrt-div_binary64_436 distribute-lft-out_binary64_370 count-2_binary64_367 flip-+_binary64_393 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 distribute-rgt-out_binary64_372
1×pow1/2_binary64_499 sum-log_binary64_510 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 +-commutative_binary64_349
Counts
2 → 32
Calls

4 calls:

4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
4.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
0.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
0.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))

series61.0ms (0.3%)

Counts
2 → 6
Calls

2 calls:

31.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
30.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Compiler

Compiled 64 to 64 computations (0% saved)

simplify98.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 0 (88.0ms)

IterNodesCost
04788334
14788334

prune151.0ms (0.7%)

Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New302454
Fresh022
Picked000
Done112
Total312758
Error
0.2b
Counts
58 → 27
Compiler

Compiled 537 to 258 computations (52% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))

rewrite8.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64_441
6×associate-*l*_binary64_360
4×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 sqrt-prod_binary64_435
3×associate-*r*_binary64_359 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×unswap-sqr_binary64_387
1×pow-prod-down_binary64_490 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
Counts
1 → 22
Calls

2 calls:

6.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

30.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify73.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04863270
14863270

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64_441
6×associate-*r*_binary64_359
4×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 sqrt-prod_binary64_435
3×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×unswap-sqr_binary64_387
1×pow-prod-down_binary64_490 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

30.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 24 to 24 computations (0% saved)

simplify44.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05010211

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite15.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
19×sqrt-prod_binary64_435
17×add-sqr-sqrt_binary64_441
15×associate-*r*_binary64_359
11×*-un-lft-identity_binary64_419
9×add-cube-cbrt_binary64_454
6×associate-*l*_binary64_360
5×pow1_binary64_480
4×unswap-sqr_binary64_387
3×pow-prod-down_binary64_490 distribute-lft-out_binary64_370 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 distribute-rgt-out_binary64_372
2×sqrt-div_binary64_436 pow1/2_binary64_499 associate-*r/_binary64_361 sqrt-pow1_binary64_437
1×flip3-+_binary64_422 sqrt-unprod_binary64_439 add-log-exp_binary64_458 distribute-rgt1-in_binary64_375 prod-exp_binary64_468 cbrt-unprod_binary64_452 count-2_binary64_367 *-commutative_binary64_350 flip-+_binary64_393 distribute-lft1-in_binary64_374
Counts
1 → 41
Calls

2 calls:

12.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify84.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
04778527
14778527

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

30.4b
(log.f64 (*.f64 x (+.f64 x x)))
29.4b
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
2.8b
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
2.8b
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
29.4b
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
30.4b
(log.f64 (*.f64 x (+.f64 x x)))

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
13×pow1_binary64_480
10×exp-prod_binary64_471
7×add-sqr-sqrt_binary64_441
6×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r/_binary64_361 log-pow_binary64_508 add-exp-log_binary64_457 sqrt-pow1_binary64_437 log-div_binary64_506
4×exp-diff_binary64_467 sqrt-prod_binary64_435
3×flip3-+_binary64_422 pow-prod-down_binary64_490 add-log-exp_binary64_458 log-prod_binary64_505 flip-+_binary64_393 add-cbrt-cube_binary64_455
2×sqrt-div_binary64_436 rem-log-exp_binary64_460 exp-sum_binary64_465
1×pow1/2_binary64_499 prod-exp_binary64_468 rem-exp-log_binary64_459 rem-sqrt-square_binary64_432
Counts
3 → 51
Calls

6 calls:

7.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
6.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
5.0ms
(log.f64 (*.f64 x (+.f64 x x)))
0.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
0.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))

series241.0ms (1.1%)

Counts
3 → 9
Calls

3 calls:

102.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
80.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
60.0ms
(log.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 186 to 186 computations (0% saved)

simplify95.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
04857585
14857585

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

1.1b
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
0.0b
(pow.f64 (exp.f64 (*.f64 x x)) 2)
0.0b
(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)))
0.0b
(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)))
0.0b
(pow.f64 (exp.f64 (*.f64 x x)) 2)
1.1b
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))

rewrite12.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×add-sqr-sqrt_binary64_441
8×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 log-prod_binary64_505
6×unpow-prod-down_binary64_498
5×pow1_binary64_480
4×add-log-exp_binary64_458 add-exp-log_binary64_457 sqrt-prod_binary64_435
3×rem-log-exp_binary64_460 add-cbrt-cube_binary64_455 pow-pow_binary64_491 pow-unpow_binary64_496
2×pow-exp_binary64_487 sqr-pow_binary64_391 log-pow_binary64_508 pow-to-exp_binary64_488 unpow2_binary64_484
1×pow1/2_binary64_499 exp-to-pow_binary64_481 exp-prod_binary64_471 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432
Counts
3 → 53
Calls

6 calls:

3.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)
3.0ms
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
1.0ms
(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)))
0.0ms
(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)))
0.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)

series230.0ms (1%)

Counts
3 → 12
Calls

3 calls:

112.0ms
(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)))
89.0ms
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
29.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)
Compiler

Compiled 164 to 162 computations (1.2% saved)

simplify86.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
04977620
14977620

prune1.1s (4.8%)

Pruning

94 alts after pruning (90 fresh and 4 done)

PrunedKeptTotal
New14871219
Fresh21921
Picked000
Done246
Total15294246
Error
0.0b
Counts
246 → 94
Compiler

Compiled 2570 to 1420 computations (44.7% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
0.2b
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
16×add-exp-log_binary64_457 pow1_binary64_480
12×add-sqr-sqrt_binary64_441
10×associate-*r*_binary64_359
9×pow-prod-down_binary64_490 prod-exp_binary64_468 cbrt-unprod_binary64_452 add-cbrt-cube_binary64_455
8×cbrt-prod_binary64_450
6×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
4×associate-*l*_binary64_360 sqrt-prod_binary64_435
3×unswap-sqr_binary64_387
2×add-log-exp_binary64_458 *-commutative_binary64_350
Counts
2 → 48
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
6.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

series133.0ms (0.6%)

Counts
2 → 6
Calls

2 calls:

102.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
31.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 120 to 120 computations (0% saved)

simplify72.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
05097624

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64_441
6×associate-*r*_binary64_359
4×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 sqrt-prod_binary64_435
3×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×unswap-sqr_binary64_387
1×pow-prod-down_binary64_490 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify45.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05010211

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite16.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
19×sqrt-prod_binary64_435
17×add-sqr-sqrt_binary64_441
15×associate-*r*_binary64_359
11×*-un-lft-identity_binary64_419
9×add-cube-cbrt_binary64_454
6×associate-*l*_binary64_360
5×pow1_binary64_480
4×unswap-sqr_binary64_387
3×pow-prod-down_binary64_490 distribute-lft-out_binary64_370 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 distribute-rgt-out_binary64_372
2×sqrt-div_binary64_436 pow1/2_binary64_499 associate-*r/_binary64_361 sqrt-pow1_binary64_437
1×flip3-+_binary64_422 sqrt-unprod_binary64_439 add-log-exp_binary64_458 distribute-rgt1-in_binary64_375 prod-exp_binary64_468 cbrt-unprod_binary64_452 count-2_binary64_367 *-commutative_binary64_350 flip-+_binary64_393 distribute-lft1-in_binary64_374
Counts
1 → 41
Calls

2 calls:

13.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 42 to 42 computations (0% saved)

simplify85.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
04778527
14778527

localize6.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.3b
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
0.1b
(sqrt.f64 (*.f64 x (sqrt.f64 2)))
0.1b
(sqrt.f64 (*.f64 x (sqrt.f64 2)))
0.1b
(sqrt.f64 (*.f64 x (sqrt.f64 2)))
0.3b
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite36.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
60×pow1_binary64_480
30×sqrt-pow1_binary64_437
24×add-sqr-sqrt_binary64_441
23×pow-prod-down_binary64_490
16×associate-*r*_binary64_359
14×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
13×sqrt-prod_binary64_435
11×pow1/2_binary64_499
10×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow-prod-up_binary64_489
6×pow-sqr_binary64_392
5×unswap-sqr_binary64_387
4×add-log-exp_binary64_458 swap-sqr_binary64_386
3×prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
1×sqrt-unprod_binary64_439 rem-square-sqrt_binary64_431 pow-plus_binary64_482 pow2_binary64_500
Counts
4 → 104
Calls

8 calls:

11.0ms
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
6.0ms
(*.f64 x (sqrt.f64 2))
5.0ms
(*.f64 x (sqrt.f64 2))
3.0ms
(sqrt.f64 (*.f64 x (sqrt.f64 2)))
0.0ms
(sqrt.f64 (*.f64 x (sqrt.f64 2)))

series114.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

33.0ms
(*.f64 x (sqrt.f64 2))
30.0ms
(*.f64 x (sqrt.f64 2))
30.0ms
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
22.0ms
(sqrt.f64 (*.f64 x (sqrt.f64 2)))
Compiler

Compiled 276 to 256 computations (7.2% saved)

simplify52.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
04928837
14928837

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (cbrt.f64 x))))
0.2b
(sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
0.1b
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (cbrt.f64 x)))
0.0b
(sqrt.f64 (cbrt.f64 x))
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)

rewrite15.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod_binary64_450
23×add-sqr-sqrt_binary64_441
15×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
11×pow1_binary64_480
9×pow1/3_binary64_501
6×associate-*r*_binary64_359 swap-sqr_binary64_386 associate-*l*_binary64_360 add-exp-log_binary64_457
4×add-log-exp_binary64_458 unswap-sqr_binary64_387 add-cbrt-cube_binary64_455
2×pow-prod-down_binary64_490 pow-sqr_binary64_392 pow-prod-up_binary64_489
1×prod-exp_binary64_468 cbrt-unprod_binary64_452 pow-plus_binary64_482 *-commutative_binary64_350 pow2_binary64_500
Counts
4 → 73
Calls

8 calls:

6.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(sqrt.f64 (cbrt.f64 x))

series316.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

90.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
78.0ms
(cbrt.f64 x)
77.0ms
(cbrt.f64 x)
72.0ms
(cbrt.f64 x)
Compiler

Compiled 418 to 310 computations (25.8% saved)

simplify77.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04873548
14873548

prune3.0s (13.5%)

Pruning

184 alts after pruning (175 fresh and 9 done)

PrunedKeptTotal
New22896324
Fresh67985
Picked000
Done099
Total234184418
Error
0b
Counts
418 → 184
Compiler

Compiled 5424 to 3512 computations (35.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x)))
0.1b
(*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x))
0.1b
(*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x))
0.3b
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x)))

rewrite19.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
19×associate-*l*_binary64_360
17×add-exp-log_binary64_457
16×add-sqr-sqrt_binary64_441
10×prod-exp_binary64_468
9×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
8×unpow-prod-down_binary64_498
7×add-cbrt-cube_binary64_455 sqrt-prod_binary64_435
6×cbrt-prod_binary64_450
4×associate-*r*_binary64_359 unswap-sqr_binary64_387 cbrt-unprod_binary64_452 pow1_binary64_480
2×add-log-exp_binary64_458 pow-exp_binary64_487 sqr-pow_binary64_391 pow-to-exp_binary64_488 *-commutative_binary64_350
1×pow-prod-down_binary64_490
Counts
2 → 54
Calls

4 calls:

9.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x)))
6.0ms
(*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x))
0.0ms
(*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x))
0.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x)))

series152.0ms (0.7%)

Counts
2 → 6
Calls

2 calls:

121.0ms
(*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x))
30.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (fabs.f64 x)))
Compiler

Compiled 108 to 108 computations (0% saved)

simplify71.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
04987755
14987755

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64_441
6×associate-*r*_binary64_359
4×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 sqrt-prod_binary64_435
3×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×unswap-sqr_binary64_387
1×pow-prod-down_binary64_490 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 36 to 36 computations (0% saved)

simplify47.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05010211

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

30.4b
(log.f64 (*.f64 x (+.f64 x x)))
29.4b
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
2.8b
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
2.8b
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
29.4b
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
30.4b
(log.f64 (*.f64 x (+.f64 x x)))

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
13×pow1_binary64_480
10×exp-prod_binary64_471
7×add-sqr-sqrt_binary64_441
6×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r/_binary64_361 log-pow_binary64_508 add-exp-log_binary64_457 sqrt-pow1_binary64_437 log-div_binary64_506
4×exp-diff_binary64_467 sqrt-prod_binary64_435
3×flip3-+_binary64_422 pow-prod-down_binary64_490 add-log-exp_binary64_458 log-prod_binary64_505 flip-+_binary64_393 add-cbrt-cube_binary64_455
2×sqrt-div_binary64_436 rem-log-exp_binary64_460 exp-sum_binary64_465
1×pow1/2_binary64_499 prod-exp_binary64_468 rem-exp-log_binary64_459 rem-sqrt-square_binary64_432
Counts
3 → 51
Calls

6 calls:

7.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
6.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
5.0ms
(log.f64 (*.f64 x (+.f64 x x)))
0.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
0.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))

series239.0ms (1.1%)

Counts
3 → 9
Calls

3 calls:

97.0ms
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 x x)))))
78.0ms
(exp.f64 (log.f64 (*.f64 x (+.f64 x x))))
64.0ms
(log.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 204 to 204 computations (0% saved)

simplify97.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
04857585
14857585

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.5b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))) (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))))
0.1b
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))
0.1b
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))
0.1b
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))
0.5b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))) (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))))
0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))

rewrite34.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
60×pow1_binary64_480
30×sqrt-pow1_binary64_437
24×add-sqr-sqrt_binary64_441
23×pow-prod-down_binary64_490
16×associate-*l*_binary64_360
14×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
13×sqrt-prod_binary64_435
11×pow1/2_binary64_499
10×associate-*r*_binary64_359 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow-prod-up_binary64_489
6×pow-sqr_binary64_392
5×unswap-sqr_binary64_387
4×add-log-exp_binary64_458 swap-sqr_binary64_386
3×prod-exp_binary64_468 cbrt-unprod_binary64_452 *-commutative_binary64_350
1×sqrt-unprod_binary64_439 rem-square-sqrt_binary64_431 pow-plus_binary64_482 pow2_binary64_500
Counts
4 → 104
Calls

8 calls:

11.0ms
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))) (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))))
6.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
6.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
3.0ms
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))
0.0ms
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))

series132.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

43.0ms
(sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x)))
32.0ms
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))) (sqrt.f64 (*.f64 (sqrt.f64 2) (fabs.f64 x))))
30.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
28.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
Compiler

Compiled 264 to 228 computations (13.6% saved)

simplify63.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
051171031

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 x))))))
0.2b
(sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
0.1b
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 x)))))
0.0b
(sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 x))))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
2.1b
(exp.f64 (log.f64 (cbrt.f64 x)))

rewrite11.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×cbrt-prod_binary64_450
10×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
6×log-prod_binary64_505 exp-sum_binary64_465
5×exp-prod_binary64_471 pow1_binary64_480
4×pow1/3_binary64_501 add-log-exp_binary64_458 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
2×log-pow_binary64_508
1×rem-exp-log_binary64_459
Counts
4 → 52
Calls

8 calls:

3.0ms
(exp.f64 (log.f64 (cbrt.f64 x)))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 x))))

series354.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

133.0ms
(exp.f64 (log.f64 (cbrt.f64 x)))
76.0ms
(cbrt.f64 x)
73.0ms
(cbrt.f64 x)
73.0ms
(cbrt.f64 x)
Compiler

Compiled 476 to 356 computations (25.2% saved)

simplify85.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
04892332
14892332

prune3.8s (16.8%)

Pruning

266 alts after pruning (252 fresh and 14 done)

PrunedKeptTotal
New22897325
Fresh15155170
Picked000
Done01414
Total243266509
Error
0b
Counts
509 → 266
Compiler

Compiled 3039 to 1676 computations (44.9% saved)

simplify167.0ms (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0151410973
1151410973

regimes2.1s (9.2%)

Compiler

Compiled 17854 to 13526 computations (24.2% saved)

bsearch0.0ms (0%)

regimes1.5s (6.6%)

Compiler

Compiled 13654 to 10226 computations (25.1% saved)

bsearch0.0ms (0%)

regimes556.0ms (2.5%)

Compiler

Compiled 4030 to 3192 computations (20.8% saved)

bsearch0.0ms (0%)

regimes543.0ms (2.4%)

Compiler

Compiled 3950 to 3120 computations (21% saved)

bsearch0.0ms (0%)

regimes144.0ms (0.6%)

Compiler

Compiled 424 to 323 computations (23.8% saved)

bsearch13.0ms (0.1%)

Steps
ItersRangePoint
9
-1.0316202792135276e-305
3.248816851435269e-305
-3.1772341154775e-311
Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.1%)

Compiler

Compiled 8 to 10 computations (-25% saved)

bsearch13.0ms (0.1%)

Steps
ItersRangePoint
10
-2.745612790798169e-194
-2.0721744500342595e-212
-3.559042902657881e-206
Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0%)

Accuracy

Total 0.3b remaining (100%)

Threshold costs 0.3b (100%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch6.0ms (0%)

Compiler

Compiled 68 to 67 computations (1.5% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
061109
161109

end0.0ms (0%)

sample5.6s (24.7%)

Algorithm
1×intervals
Results
184.0ms8000×body128valid
0.0ms1×body128invalid
Compiler

Compiled 4491 to 3431 computations (23.6% saved)

Pareto

0.8383585965875182

Profiling

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