Details

Time bar (total: 2.2s)

analyze70.0ms (3.2%)

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
50%50%0.1%6
56.2%37.5%6.3%7
68.7%25%6.3%8
71.8%18.7%9.5%9
78%12.5%9.5%10
79.6%9.4%11%11
82.7%6.2%11%12
83.6%4.6%11.8%13
85.1%3.1%11.8%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample15.0ms (0.7%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
0.0ms2×body128invalid
Compiler

Compiled 23 to 23 computations (0% saved)

simplify118.0ms (5.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
056413
156413

prune4.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0b
Counts
2 → 2
Compiler

Compiled 29 to 26 computations (10.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 y (+.f64 x -1/2)) x)
0.0b
(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
0.0b
(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
0.0b
(-.f64 (*.f64 y (+.f64 x -1/2)) x)

rewrite19.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
9×add-log-exp_binary64_2163
6×cancel-sign-sub-inv_binary64_2090 associate-+l+_binary64_2057 *-un-lft-identity_binary64_2124
4×add-cube-cbrt_binary64_2159 add-sqr-sqrt_binary64_2146 associate--l+_binary64_2061
2×sum-log_binary64_2215 pow1_binary64_2185 diff-log_binary64_2216 distribute-rgt-in_binary64_2074 sub-neg_binary64_2117 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 distribute-lft-in_binary64_2073
1×flip--_binary64_2099 flip3--_binary64_2128 associate-+l-_binary64_2059 distribute-lft-out_binary64_2075 +-commutative_binary64_2054 flip3-+_binary64_2127 flip-+_binary64_2098
Counts
2 → 36
Calls

4 calls:

9.0ms
(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
6.0ms
(-.f64 (*.f64 y (+.f64 x -1/2)) x)
0.0ms
(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
0.0ms
(-.f64 (*.f64 y (+.f64 x -1/2)) x)

series194.0ms (9%)

Counts
2 → 24
Calls

2 calls:

101.0ms
(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
93.0ms
(-.f64 (*.f64 y (+.f64 x -1/2)) x)
Compiler

Compiled 338 to 294 computations (13% saved)

simplify64.0ms (3%)

Algorithm
1×egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04951710
14951710

prune47.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New60060
Fresh011
Picked011
Done000
Total60262
Error
0b
Counts
62 → 2
Compiler

Compiled 692 to 464 computations (32.9% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 x (-.f64 y 1))
0.0b
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 8277062471433911/9007199254740992)
0.0b
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 8277062471433911/9007199254740992)
0.0b
(*.f64 x (-.f64 y 1))

rewrite26.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_2146
13×cancel-sign-sub-inv_binary64_2090 *-un-lft-identity_binary64_2124
10×associate-+l+_binary64_2057
8×add-cube-cbrt_binary64_2159 distribute-rgt-in_binary64_2074 associate--l+_binary64_2061 distribute-lft-in_binary64_2073
7×add-log-exp_binary64_2163 associate-*r*_binary64_2064
5×sub-neg_binary64_2117
4×pow1_binary64_2185 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
3×associate-*l*_binary64_2065
2×difference-of-squares_binary64_2093 sum-log_binary64_2215 associate-*r/_binary64_2066
1×flip--_binary64_2099 pow-prod-down_binary64_2195 flip3--_binary64_2128 unswap-sqr_binary64_2092 associate-+l-_binary64_2059 distribute-lft-out--_binary64_2076 *-commutative_binary64_2055 distribute-lft-out_binary64_2075 diff-log_binary64_2216 prod-exp_binary64_2173 +-commutative_binary64_2054 flip3-+_binary64_2127 difference-of-sqr-1_binary64_2094 flip-+_binary64_2098 cbrt-unprod_binary64_2157
Counts
2 → 56
Calls

4 calls:

11.0ms
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 8277062471433911/9007199254740992)
8.0ms
(*.f64 x (-.f64 y 1))
0.0ms
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 8277062471433911/9007199254740992)
0.0ms
(*.f64 x (-.f64 y 1))

series170.0ms (7.8%)

Counts
2 → 21
Calls

2 calls:

107.0ms
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 8277062471433911/9007199254740992)
63.0ms
(*.f64 x (-.f64 y 1))
Compiler

Compiled 323 to 281 computations (13% saved)

simplify68.0ms (3.1%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
05040798

prune56.0ms (2.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New77077
Fresh000
Picked011
Done011
Total77279
Error
0b
Counts
79 → 2
Compiler

Compiled 990 to 669 computations (32.4% saved)

simplify4.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06785
16785

regimes35.0ms (1.6%)

Compiler

Compiled 124 to 136 computations (-9.7% saved)

bsearch0.0ms (0%)

regimes62.0ms (2.9%)

Compiler

Compiled 84 to 100 computations (-19% saved)

bsearch26.0ms (1.2%)

Steps
ItersRangePoint
9
0.6400884701246073
2061467280.7300844
156.28846301531888
5
-103822685.83788441
-29726585.25488291
-30191952.726829603
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes60.0ms (2.8%)

Compiler

Compiled 70 to 88 computations (-25.7% saved)

bsearch24.0ms (1.1%)

Steps
ItersRangePoint
9
0.6400884701246073
2061467280.7300844
69329.01949494769
5
-103822685.83788441
-29726585.25488291
-41721232.55595331
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes56.0ms (2.6%)

Compiler

Compiled 56 to 74 computations (-32.1% saved)

bsearch25.0ms (1.1%)

Steps
ItersRangePoint
4
0.3809761429873134
0.6400884701246073
0.5337376683324252
10
-29726585.25488291
-0.0003251330800606758
-0.7439831696747088
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes53.0ms (2.4%)

Compiler

Compiled 46 to 64 computations (-39.1% saved)

bsearch24.0ms (1.1%)

Steps
ItersRangePoint
4
0.3809761429873134
0.6400884701246073
0.6282717143699204
10
-29726585.25488291
-0.0003251330800606758
-0.7439831696747088
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes56.0ms (2.6%)

Compiler

Compiled 36 to 56 computations (-55.6% saved)

bsearch28.0ms (1.3%)

Steps
ItersRangePoint
9
0.023951678011460076
231641.11253109007
1.5457092694642443
8
-621.3516607826381
-0.0572461978526713
-1.3534290142820549
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes43.0ms (2%)

Compiler

Compiled 26 to 46 computations (-76.9% saved)

bsearch26.0ms (1.2%)

Steps
ItersRangePoint
10
2.1984246630671487e-12
0.3809761429873134
5.403764690913501e-09
5
-103822685.83788441
-29726585.25488291
-30191952.726829603
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.8%)

Compiler

Compiled 16 to 34 computations (-112.5% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.8%)

Accuracy

Total 0.0b remaining (89.1%)

Threshold costs 0.0b (89.1%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch9.0ms (0.4%)

Compiler

Compiled 153 to 115 computations (24.8% saved)

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
089199
189199

end0.0ms (0%)

sample724.0ms (33.4%)

Algorithm
1×intervals
Results
247.0ms7998×body128valid
2.0ms69×body128invalid
0.0ms1×body1024valid
0.0ms1×body512valid
Compiler

Compiled 209 to 189 computations (9.6% saved)

Pareto

0.6104209391345656

Profiling

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