Details

Time bar (total: 2.2s)

analyze73.0ms (3.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
25%40.6%34.4%7
31.2%25%43.8%8
39%17.2%43.8%9
42.9%13.3%43.8%10
47.2%9%43.8%11
49.4%6.8%43.8%12
51.6%4.6%43.8%13
52.7%3.5%43.8%14
Compiler

Compiled 12 to 9 computations (25% saved)

sample14.0ms (0.6%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify8.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02413
12413

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 2
Compiler

Compiled 49 to 37 computations (24.5% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))

rewrite8.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
6×add-log-exp_binary64
3×sum-log_binary64
1×flip3-+_binary64 *-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64 associate-+l+_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64 +-commutative_binary64 flip-+_binary64
Counts
1 → 13
Calls

1 calls:

7.0ms
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))

series39.0ms (1.8%)

Counts
1 → 3
Calls

1 calls:

39.0ms
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))

simplify64.0ms (3%)

Algorithm
1×egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04960281
14960281

prune28.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New14216
Fresh011
Picked011
Done000
Total14418

Merged error: 0b

Counts
18 → 4
Compiler

Compiled 486 to 300 computations (38.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))
0.0b
(*.f64 x (+.f64 x 2))

rewrite17.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
6×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
4×add-log-exp_binary64 pow1_binary64 associate-*r*_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-*l*_binary64
2×flip3-+_binary64 associate-*r/_binary64 associate-+l+_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 flip-+_binary64
1×pow-prod-down_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 unswap-sqr_binary64 prod-exp_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
2 → 36
Calls

2 calls:

7.0ms
(*.f64 x (+.f64 x 2))
7.0ms
(+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))

series94.0ms (4.3%)

Counts
2 → 6
Calls

2 calls:

54.0ms
(*.f64 x (+.f64 x 2))
39.0ms
(+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))

simplify69.0ms (3.2%)

Algorithm
1×egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
05453509

prune30.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New42042
Fresh022
Picked011
Done011
Total42446

Merged error: 0b

Counts
46 → 4
Compiler

Compiled 619 to 328 computations (47% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))
0.0b
(*.f64 x (+.f64 x 2))
0.0b
(*.f64 x (+.f64 x 2))
0.1b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))) (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))))

rewrite48.0ms (2.2%)

Algorithm
1×rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
23×pow1_binary64
20×*-un-lft-identity_binary64
18×sqrt-prod_binary64
16×add-cube-cbrt_binary64
14×associate-*r*_binary64
12×associate-*l*_binary64 sqrt-div_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
9×flip3-+_binary64 flip-+_binary64
8×pow1/2_binary64 swap-sqr_binary64 sqrt-pow1_binary64
6×add-log-exp_binary64 associate-*r/_binary64 unswap-sqr_binary64
5×pow-prod-down_binary64 pow-prod-up_binary64
4×frac-times_binary64
3×cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 prod-exp_binary64 pow-sqr_binary64 *-commutative_binary64
2×distribute-lft-out_binary64 rem-sqrt-square_binary64 associate-+r+_binary64 associate-*l/_binary64
1×rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 sqr-abs_binary64 +-commutative_binary64 pow2_binary64 sum-log_binary64
Counts
4 → 117
Calls

4 calls:

17.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))) (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))))
7.0ms
(*.f64 x (+.f64 x 2))
7.0ms
(*.f64 x (+.f64 x 2))
5.0ms
(+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))

series198.0ms (9.2%)

Counts
4 → 12
Calls

4 calls:

54.0ms
(*.f64 x (+.f64 x 2))
54.0ms
(*.f64 x (+.f64 x 2))
46.0ms
(+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))
45.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))) (sqrt.f64 (+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))))

simplify76.0ms (3.5%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
050541982

prune145.0ms (6.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1290129
Fresh011
Picked011
Done022
Total1294133

Merged error: 0b

Counts
133 → 4
Compiler

Compiled 3123 to 1775 computations (43.2% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2))))
0.1b
(*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))
2.7b
(-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4))
27.7b
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))

rewrite95.0ms (4.4%)

Algorithm
1×rewrite-expression-head
Rules
28×associate-*r/_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
18×pow1_binary64
17×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64 add-cube-cbrt_binary64
12×flip3-+_binary64 flip-+_binary64
9×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64 times-frac_binary64
8×frac-times_binary64 associate--l+_binary64
7×cancel-sign-sub-inv_binary64
6×add-log-exp_binary64 associate-*l*_binary64
4×associate-*l/_binary64
3×associate-/r*_binary64 flip3--_binary64 unpow-prod-down_binary64 associate-/l*_binary64 flip--_binary64
2×associate-/l/_binary64 associate-*r*_binary64 associate-/r/_binary64 *-commutative_binary64
1×sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 sqr-pow_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 126
Calls

4 calls:

28.0ms
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))
19.0ms
(-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4))
15.0ms
(*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2))))
13.0ms
(*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))

series262.0ms (12.1%)

Counts
4 → 12
Calls

4 calls:

110.0ms
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))
98.0ms
(-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))) (pow.f64 y 4))
28.0ms
(*.f64 x (*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2))))
25.0ms
(*.f64 x (*.f64 (+.f64 x 2) (+.f64 x 2)))

simplify77.0ms (3.6%)

Algorithm
1×egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049603193
149603193

prune215.0ms (10%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1380138
Fresh000
Picked011
Done033
Total1384142

Merged error: 0b

Counts
142 → 4
Compiler

Compiled 4545 to 2853 computations (37.2% saved)

regimes66.0ms (3.1%)

Compiler

Compiled 376 to 277 computations (26.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11113

end0.0ms (0%)

sample491.0ms (22.7%)

Algorithm
1×intervals
Results
246.0ms8000×body128valid
0.0ms1×body128invalid
Compiler

Compiled 98 to 73 computations (25.5% saved)

Profiling

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