Details

Time bar (total: 2.8s)

analyze12.0ms (0.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample234.0ms (8.5%)

Algorithm
intervals
Results
225.0ms256×body128valid
Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify124.0ms (4.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
046617
146617

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite40.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
49×times-frac_binary64
30×sqrt-prod_binary64
26×add-cube-cbrt_binary64
18×difference-of-squares_binary64
13×distribute-lft-out_binary64
distribute-lft-out--_binary64
associate-/l*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
associate-/r*_binary64 pow1_binary64 associate-/r/_binary64
add-log-exp_binary64
flip3-+_binary64 associate-/l/_binary64 rem-sqrt-square_binary64 div-inv_binary64 flip-+_binary64
pow1/2_binary64 flip3--_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 flip--_binary64 sqrt-div_binary64
Counts
3 → 100
Calls

3 calls:

11.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series67.0ms (2.4%)

Counts
3 → 15
Calls

3 calls:

27.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
21.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
19.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
Compiler

Compiled 231 to 225 computations (2.6% saved)

simplify77.0ms (2.8%)

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
064982045

prune132.0ms (4.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1132115
Fresh000
Picked101
Done000
Total1142116

Merged error: 0b

Counts
116 → 2
Compiler

Compiled 2021 to 1630 computations (19.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))
0.0b
(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
0.0b
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))

rewrite60.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt_binary64
81×*-un-lft-identity_binary64
61×times-frac_binary64
50×difference-of-squares_binary64
36×associate-*l*_binary64
32×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
flip3--_binary64 flip--_binary64
associate-*r*_binary64 cancel-sign-sub-inv_binary64 associate-/l*_binary64
associate-/r*_binary64 sqrt-div_binary64
add-log-exp_binary64 associate-*r/_binary64 distribute-lft-in_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 frac-times_binary64
pow-prod-down_binary64 associate-/l/_binary64 sub-neg_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 associate-*l/_binary64
pow1/2_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 sqrt-prod_binary64 *-commutative_binary64
Counts
4 → 151
Calls

4 calls:

20.0ms
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))
15.0ms
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))
9.0ms
(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
1.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))

series84.0ms (3%)

Counts
4 → 21
Calls

4 calls:

23.0ms
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))
23.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))
20.0ms
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))
18.0ms
(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
Compiler

Compiled 358 to 340 computations (5% saved)

simplify59.0ms (2.1%)

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
049483307
149483307

prune218.0ms (7.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1720172
Fresh011
Picked011
Done000
Total1722174

Merged error: 0b

Counts
174 → 2
Compiler

Compiled 3949 to 2833 computations (28.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite88.0ms (3.2%)

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt_binary64
149×*-un-lft-identity_binary64
127×times-frac_binary64
83×sqrt-prod_binary64
62×add-cube-cbrt_binary64
48×associate-*r*_binary64
30×difference-of-squares_binary64
28×add-exp-log_binary64
27×associate-*l*_binary64
18×distribute-lft-out_binary64 add-cbrt-cube_binary64
15×unswap-sqr_binary64 distribute-lft-out--_binary64
10×sqrt-div_binary64
div-exp_binary64
pow1_binary64 prod-exp_binary64
associate-/r*_binary64
associate-/r/_binary64 associate-/l*_binary64
flip3-+_binary64 cbrt-undiv_binary64 flip-+_binary64
add-log-exp_binary64 cbrt-unprod_binary64
div-inv_binary64
associate-/l/_binary64 pow1/2_binary64 1-exp_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 rec-exp_binary64
pow-prod-down_binary64 flip3--_binary64 associate-*r/_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 218
Calls

4 calls:

44.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
10.0ms
(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
3.0ms
(sqrt.f64 (+.f64 1 x))
3.0ms
(sqrt.f64 (+.f64 1 x))

series86.0ms (3.1%)

Counts
4 → 24
Calls

4 calls:

25.0ms
(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
22.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
19.0ms
(sqrt.f64 (+.f64 1 x))
19.0ms
(sqrt.f64 (+.f64 1 x))
Compiler

Compiled 582 to 526 computations (9.6% saved)

simplify100.0ms (3.6%)

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049414422
149414422

prune420.0ms (15.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2420242
Fresh000
Picked011
Done011
Total2422244

Merged error: 0b

Counts
244 → 2
Compiler

Compiled 5937 to 4930 computations (17% saved)

regimes153.0ms (5.6%)

Compiler

Compiled 1349 to 1219 computations (9.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03426
13426

end0.0ms (0%)

sample772.0ms (27.9%)

Algorithm
intervals
Results
370.0ms8000×body128valid
Compiler

Compiled 246 to 220 computations (10.6% saved)

Profiling

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