Details

Time bar (total: 3.5s)

analyze94.0ms (2.7%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07111
17111
011
111
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample30.0ms (0.9%)

Algorithm
1×intervals
Results
12.0ms68×body2048valid
5.0ms38×body1024valid
4.0ms135×body128valid
1.0ms9×body512valid
0.0ms6×body256valid
Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07111
17111

prune7.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.0b
Counts
2 → 1
Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(atan.f64 (+.f64 N 1))
1.7b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite27.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
12.2b
Rules
5×add-sqr-sqrt_binary64_2146 *-un-lft-identity_binary64_2124
4×add-log-exp_binary64_2163
3×add-cube-cbrt_binary64_2159 cancel-sign-sub-inv_binary64_2090
2×pow1_binary64_2185 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
1×diff-atan_binary64_2281 diff-log_binary64_2216 flip3--_binary64_2128 sub-neg_binary64_2117 flip--_binary64_2099 difference-of-squares_binary64_2093 distribute-lft-out--_binary64_2076
Counts
2 → 24
Calls

2 calls:

4.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
(atan.f64 (+.f64 N 1))
Compiler

Compiled 348 to 227 computations (34.8% saved)

series28.0ms (0.8%)

Error
14.0b
Counts
2 → 6
Calls

2 calls:

17.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
8.0ms
(atan.f64 (+.f64 N 1))
Compiler

Compiled 126 to 98 computations (22.2% saved)

simplify77.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04998391
14998391

prune24.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New28230
Fresh000
Picked101
Done000
Total29231
Error
0.3b
Counts
31 → 2
Compiler

Compiled 360 to 237 computations (34.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 N (+.f64 N 1))
0.3b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite42.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
0.3b
Rules
6×add-sqr-sqrt_binary64_2146 *-un-lft-identity_binary64_2124
4×pow1_binary64_2185 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 add-cube-cbrt_binary64_2159 associate-*r*_binary64_2064
3×associate-*l*_binary64_2065
2×add-log-exp_binary64_2163 associate-*r/_binary64_2066
1×pow-prod-down_binary64_2195 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 unswap-sqr_binary64_2092 distribute-rgt-in_binary64_2074 distribute-lft-in_binary64_2073 flip3-+_binary64_2127 flip-+_binary64_2098 distribute-lft-out_binary64_2075 *-commutative_binary64_2055
Counts
2 → 30
Calls

2 calls:

7.0ms
(*.f64 N (+.f64 N 1))
1.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 468 to 361 computations (22.9% saved)

series57.0ms (1.6%)

Error
0.3b
Counts
2 → 9
Calls

2 calls:

37.0ms
(*.f64 N (+.f64 N 1))
13.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 200 to 174 computations (13% saved)

simplify75.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04927392
14927392

prune37.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New36339
Fresh101
Picked011
Done000
Total37441
Error
0.3b
Counts
41 → 4
Compiler

Compiled 563 to 350 computations (37.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N))))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))

rewrite131.0ms (3.8%)

Algorithm
1×rewrite-expression-head
Error
0.3b
Rules
39×cbrt-prod_binary64_2155
23×add-sqr-sqrt_binary64_2146
22×*-un-lft-identity_binary64_2124
18×cbrt-div_binary64_2156
15×add-cube-cbrt_binary64_2159
11×pow1_binary64_2185
9×pow1/3_binary64_2206 flip3-+_binary64_2127 flip-+_binary64_2098
8×swap-sqr_binary64_2091 associate-*l*_binary64_2065 associate-*r*_binary64_2064
7×distribute-rgt1-in_binary64_2080 distribute-rgt-out_binary64_2077
6×add-exp-log_binary64_2162
4×add-log-exp_binary64_2163 add-cbrt-cube_binary64_2160 frac-times_binary64_2134 unswap-sqr_binary64_2092
2×pow-prod-down_binary64_2195 pow-prod-up_binary64_2194 pow-sqr_binary64_2097 associate-*l/_binary64_2067 associate-*r/_binary64_2066
1×pow2_binary64_2205 pow-plus_binary64_2187 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 *-commutative_binary64_2055
Counts
4 → 99
Calls

4 calls:

13.0ms
(*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N))))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
Compiler

Compiled 3310 to 810 computations (75.5% saved)

series316.0ms (9.1%)

Error
0.3b
Counts
4 → 40
Calls

4 calls:

68.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
66.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
65.0ms
(*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N))))
63.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
Compiler

Compiled 2723 to 1816 computations (33.3% saved)

simplify80.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
064692507

prune155.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1381139
Fresh022
Picked011
Done011
Total1385143
Error
0.3b
Counts
143 → 5
Compiler

Compiled 4150 to 1542 computations (62.8% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
16.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))

rewrite92.0ms (2.7%)

Algorithm
1×rewrite-expression-head
Error
0.3b
Rules
20×cbrt-prod_binary64_2155
12×*-un-lft-identity_binary64_2124
8×add-cube-cbrt_binary64_2159 cbrt-div_binary64_2156 add-sqr-sqrt_binary64_2146
4×pow1/3_binary64_2206 pow1_binary64_2185 add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 flip3-+_binary64_2127 flip-+_binary64_2098 distribute-rgt1-in_binary64_2080 distribute-rgt-out_binary64_2077
Counts
4 → 60
Calls

4 calls:

3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
Compiler

Compiled 2564 to 660 computations (74.3% saved)

series332.0ms (9.6%)

Error
0.3b
Counts
4 → 40
Calls

4 calls:

68.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
67.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
65.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
64.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
Compiler

Compiled 3808 to 2180 computations (42.8% saved)

simplify76.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
050691748

prune140.0ms (4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1000100
Fresh022
Picked011
Done022
Total1005105
Error
0.3b
Counts
105 → 5
Compiler

Compiled 4172 to 1411 computations (66.2% saved)

regimes109.0ms (3.2%)

Accuracy

Total 0.0b remaining (13.4%)

Threshold costs 0.0b (13.4%)

Compiler

Compiled 1299 to 866 computations (33.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
11113

end0.0ms (0%)

sample1.5s (42.8%)

Algorithm
1×intervals
Results
353.0ms2077×body2048valid
142.0ms4105×body128valid
129.0ms1040×body1024valid
49.0ms512×body512valid
17.0ms266×body256valid
Compiler

Compiled 649 to 434 computations (33.1% saved)

Profiling

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