Details

Time bar (total: 3.2s)

analyze267.0ms (8.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%50%25%4
25%37.5%37.5%5
25%31.2%43.8%6
25%28.1%46.9%7
25%26.5%48.5%8
25%25.8%49.2%9
25%25.4%49.6%10
25%25.2%49.8%11
25%25.1%49.9%12
25%25%50%13
25%25%50%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample58.0ms (1.8%)

Algorithm
intervals
Results
16.0ms86×body2560nan
11.0ms74×body1280nan
11.0ms256×body80valid
5.0ms17×body320nan
4.0ms36×body640nan
1.0ms12×body160nan
0.0ms10×body80nan
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify335.0ms (10.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (321.0ms)

IterNodesCost
0500214

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.1b

Counts
2 → 1
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
29.9b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite16.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64 sqrt-prod_binary64
add-sqr-sqrt_binary64
add-log-exp_binary64
pow1_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 difference-of-squares_binary64 insert-posit16 sqrt-div_binary64
flip3-+_binary64 pow1/2_binary64 flip3--_binary64 distribute-lft-out_binary64 difference-of-sqr-1_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 sum-log_binary64
Counts
2 → 32
Calls

2 calls:

9.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
6.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

series96.0ms (3%)

Counts
2 → 6
Calls

2 calls:

52.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
44.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify92.0ms (2.9%)

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
04908561
14908561

prune36.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New37138
Fresh000
Picked101
Done000
Total38139

Merged error: 0b

Counts
39 → 1
Compiler

Compiled 551 to 364 computations (33.9% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite22.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
15×sqrt-prod_binary64
12×sqrt-div_binary64
11×*-un-lft-identity_binary64
10×associate-*r*_binary64
associate-*l*_binary64
pow1_binary64 add-cube-cbrt_binary64
flip3-+_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64 flip-+_binary64 frac-times_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64
pow1/2_binary64 associate-*r/_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 insert-posit16 associate-*l/_binary64
cbrt-unprod_binary64 distribute-lft-out_binary64 difference-of-sqr-1_binary64 sqrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
2 → 56
Calls

2 calls:

15.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series136.0ms (4.3%)

Counts
2 → 6
Calls

2 calls:

70.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
66.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify148.0ms (4.7%)

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (123.0ms)

IterNodesCost
049021223
149021223

prune67.0ms (2.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New62062
Fresh000
Picked011
Done000
Total62163

Merged error: 0b

Counts
63 → 1
Compiler

Compiled 1185 to 895 computations (24.5% saved)

simplify6.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02419
12419

end0.0ms (0%)

sample1.9s (59%)

Algorithm
intervals
Results
575.0ms2950×body2560nan
397.0ms2483×body1280nan
340.0ms8000×body80valid
152.0ms1193×body640nan
57.0ms591×body320nan
21.0ms310×body160nan
10.0ms288×body80nan
Compiler

Compiled 34 to 29 computations (14.7% saved)

Profiling

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