Details

Time bar (total: 2.9s)

analyze260.0ms (9%)

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)

sample52.0ms (1.8%)

Algorithm
intervals
Results
21.0ms123×body2048nan
11.0ms256×body128valid
7.0ms62×body1024nan
2.0ms28×body512nan
1.0ms13×body256nan
0.0ms15×body128nan
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify294.0ms (10.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (129.0ms)

IterNodesCost
0515014

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.1b

Counts
2 → 1
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 (*.f64 x x) 1)
0.0b
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
28.0b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite20.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64_1088
add-sqr-sqrt_binary64_1109 add-log-exp_binary64_1124
sqrt-prod_binary64_1103
pow1_binary64_1146 add-cube-cbrt_binary64_1120 difference-of-squares_binary64_1057
add-cbrt-cube_binary64_1121 add-exp-log_binary64_1123
difference-of-sqr-1_binary64_1058 flip3--_binary64_1092 flip--_binary64_1063 sqrt-div_binary64_1104
rem-sqrt-square_binary64_1101 sub-neg_binary64_1081 sum-log_binary64_1176 +-commutative_binary64_1020 diff-log_binary64_1177 flip-+_binary64_1062 flip3-+_binary64_1091 distribute-lft-out_binary64_1041 sqrt-pow1_binary64_1105 pow1/2_binary64_1165
Counts
3 → 44
Calls

3 calls:

7.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms
(-.f64 (*.f64 x x) 1)

series153.0ms (5.3%)

Counts
3 → 9
Calls

3 calls:

60.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
51.0ms
(-.f64 (*.f64 x x) 1)
41.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify69.0ms (2.4%)

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04979703
14979703

prune43.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New52153
Fresh000
Picked011
Done000
Total52254

Merged error: 0b

Counts
54 → 2
Compiler

Compiled 742 to 487 computations (34.4% 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)))

rewrite23.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_1109
15×sqrt-prod_binary64_1103
12×sqrt-div_binary64_1104
11×*-un-lft-identity_binary64_1088
10×associate-*r*_binary64_1030
associate-*l*_binary64_1031
pow1_binary64_1146 add-cube-cbrt_binary64_1120
add-cbrt-cube_binary64_1121 unswap-sqr_binary64_1056 frac-times_binary64_1098 add-exp-log_binary64_1123 flip-+_binary64_1062 add-log-exp_binary64_1124 flip3-+_binary64_1091
flip3--_binary64_1092 flip--_binary64_1063 pow-prod-down_binary64_1156
associate-*l/_binary64_1033 sqrt-pow1_binary64_1105 associate-*r/_binary64_1032 difference-of-squares_binary64_1057 pow1/2_binary64_1165
*-commutative_binary64_1021 cbrt-unprod_binary64_1118 difference-of-sqr-1_binary64_1058 sum-log_binary64_1176 +-commutative_binary64_1020 sqrt-unprod_binary64_1107 prod-exp_binary64_1134 distribute-lft-out_binary64_1041 distribute-lft-out--_binary64_1042
Counts
2 → 54
Calls

2 calls:

15.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series132.0ms (4.6%)

Counts
2 → 6
Calls

2 calls:

69.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
63.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify57.0ms (2%)

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049251195
149251195

prune63.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New60060
Fresh000
Picked011
Done011
Total60262

Merged error: 0b

Counts
62 → 2
Compiler

Compiled 1149 to 865 computations (24.7% saved)

regimes27.0ms (0.9%)

Compiler

Compiled 99 to 79 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02319
12319

end0.0ms (0%)

sample1.7s (57.8%)

Algorithm
intervals
Results
628.0ms4108×body2048nan
341.0ms8000×body128valid
237.0ms1963×body1024nan
96.0ms1033×body512nan
31.0ms520×body256nan
17.0ms506×body128nan
1.0msbody4096nan
Compiler

Compiled 43 to 36 computations (16.3% saved)

Profiling

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