Details

Time bar (total: 11.0s)

analyze430.0ms (3.9%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03446
13446
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
62.4%37.5%0.1%5
62.4%37.5%0.1%6
68.7%31.2%0.1%7
68.7%31.2%0.1%8
71.8%28.1%0.1%9
71.8%28.1%0.1%10
73.4%26.5%0.1%11
73.4%26.5%0.1%12
74.1%25.8%0.1%13
74.1%25.8%0.1%14
Compiler

Compiled 16 to 13 computations (18.8% saved)

sample35.0ms (0.3%)

Algorithm
1×intervals
Results
9.0ms27×body2048valid
9.0ms193×body128valid
3.0ms11×body4096valid
2.0ms12×body1024valid
1.0ms10×body512valid
0.0ms3×body256valid
Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02323
12323

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
38.1b
Counts
2 → 1
Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 re re) (*.f64 im im))
0.2b
(+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
0.2b
(sqrt.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
28.6b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite88.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
38.0b
Rules
8×pow1_binary64_2185 add-log-exp_binary64_2163
7×*-un-lft-identity_binary64_2124
6×add-sqr-sqrt_binary64_2146
5×add-cube-cbrt_binary64_2159
4×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 flip3-+_binary64_2127 sqrt-div_binary64_2141 flip-+_binary64_2098 sqrt-prod_binary64_2140
3×sqrt-pow1_binary64_2142
2×pow1/2_binary64_2204 associate-*r/_binary64_2066 sum-log_binary64_2215 +-commutative_binary64_2054
1×rem-sqrt-square_binary64_2137 pow-prod-down_binary64_2195 distribute-lft-out_binary64_2075
Counts
4 → 51
Calls

4 calls:

9.0ms
(sqrt.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
4.0ms
(+.f64 (*.f64 re re) (*.f64 im im))
Compiler

Compiled 1296 to 455 computations (64.9% saved)

series456.0ms (4.2%)

Error
8.4b
Counts
4 → 57
Calls

4 calls:

128.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
107.0ms
(+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
82.0ms
(sqrt.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
82.0ms
(+.f64 (*.f64 re re) (*.f64 im im))
Compiler

Compiled 2292 to 1979 computations (13.7% saved)

simplify63.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
051601725

prune108.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1035108
Fresh000
Picked011
Done000
Total1036109
Error
7.9b
Counts
109 → 6
Compiler

Compiled 2017 to 1051 computations (47.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
0.9b
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
28.6b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
30.0b
(sqrt.f64 (*.f64 2 (*.f64 im im)))

rewrite174.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
7.9b
Rules
51×add-sqr-sqrt_binary64_2146
50×sqrt-prod_binary64_2140
38×*-un-lft-identity_binary64_2124
36×times-frac_binary64_2130
26×add-cube-cbrt_binary64_2159
12×difference-of-squares_binary64_2093
11×pow1_binary64_2185
9×associate-/r*_binary64_2068
6×add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 distribute-lft-out--_binary64_2076
4×sqrt-pow1_binary64_2142 sqrt-div_binary64_2141 associate-/l*_binary64_2069
3×pow-prod-down_binary64_2195 cancel-sign-sub-inv_binary64_2090
2×pow1/2_binary64_2204 flip3--_binary64_2128 flip--_binary64_2099 associate-/r/_binary64_2070
1×flip3-+_binary64_2127 flip-+_binary64_2098 rem-sqrt-square_binary64_2137 diff-log_binary64_2216 sub-neg_binary64_2117 div-exp_binary64_2175 cbrt-undiv_binary64_2158 sqrt-undiv_binary64_2145 frac-2neg_binary64_2135 clear-num_binary64_2123 div-inv_binary64_2121
Counts
4 → 108
Calls

4 calls:

15.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
9.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
5.0ms
(sqrt.f64 (*.f64 2 (*.f64 im im)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series390.0ms (3.6%)

Error
2.0b
Counts
4 → 43
Calls

4 calls:

117.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
109.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
87.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
32.0ms
(sqrt.f64 (*.f64 2 (*.f64 im im)))
Compiler

Compiled 2179 to 1713 computations (21.4% saved)

simplify81.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050214116

prune180.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1456151
Fresh044
Picked101
Done011
Total14611157
Error
2.0b
Counts
157 → 11
Compiler

Compiled 4331 to 1718 computations (60.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im))
0.4b
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im)))
0.9b
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
28.6b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite556.0ms (5.1%)

Algorithm
1×rewrite-expression-head
Error
2.0b
Rules
402×times-frac_binary64_2130
305×add-sqr-sqrt_binary64_2146
275×sqrt-prod_binary64_2140
252×*-un-lft-identity_binary64_2124
200×add-cube-cbrt_binary64_2159
52×difference-of-squares_binary64_2093
34×associate-/r*_binary64_2068
26×distribute-lft-out--_binary64_2076
15×associate-/l*_binary64_2069
11×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
9×div-inv_binary64_2121
6×add-log-exp_binary64_2163
5×pow1_binary64_2185
4×sqrt-div_binary64_2141 div-exp_binary64_2175 cbrt-undiv_binary64_2158
3×cancel-sign-sub-inv_binary64_2090
2×flip3--_binary64_2128 flip--_binary64_2099 frac-2neg_binary64_2135 clear-num_binary64_2123 associate-/l/_binary64_2071
1×pow1/2_binary64_2204 sqrt-pow1_binary64_2142 flip3-+_binary64_2127 flip-+_binary64_2098 rem-sqrt-square_binary64_2137 diff-log_binary64_2216 sub-neg_binary64_2117 associate-/r/_binary64_2070
Counts
4 → 323
Calls

4 calls:

21.0ms
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im)))
12.0ms
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im))
8.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 12437 to 3554 computations (71.4% saved)

series496.0ms (4.5%)

Error
0.5b
Counts
4 → 53
Calls

4 calls:

131.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
109.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
108.0ms
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im)))
90.0ms
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)) (fabs.f64 im))
Compiler

Compiled 2881 to 2301 computations (20.1% saved)

simplify179.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0494715883
1494715883

prune469.0ms (4.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3724376
Fresh459
Picked101
Done011
Total37710387
Error
0.5b
Counts
387 → 10
Compiler

Compiled 12554 to 3797 computations (69.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
0.2b
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))) (*.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))
0.9b
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
28.6b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite569.0ms (5.2%)

Algorithm
1×rewrite-expression-head
Error
0.5b
Rules
308×sqrt-prod_binary64_2140
183×add-sqr-sqrt_binary64_2146
162×times-frac_binary64_2130
142×*-un-lft-identity_binary64_2124
102×add-cube-cbrt_binary64_2159
87×associate-*l*_binary64_2065
40×difference-of-squares_binary64_2093
20×distribute-lft-out--_binary64_2076
18×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
10×pow1_binary64_2185
9×associate-/l*_binary64_2069 associate-/r*_binary64_2068
6×add-log-exp_binary64_2163 sqrt-div_binary64_2141 prod-exp_binary64_2173 cbrt-unprod_binary64_2157
4×associate-/r/_binary64_2070
3×flip3--_binary64_2128 flip--_binary64_2099 cancel-sign-sub-inv_binary64_2090 pow-prod-down_binary64_2195 div-exp_binary64_2175 cbrt-undiv_binary64_2158
2×div-inv_binary64_2121
1×pow1/2_binary64_2204 sqrt-pow1_binary64_2142 flip3-+_binary64_2127 flip-+_binary64_2098 rem-sqrt-square_binary64_2137 diff-log_binary64_2216 sub-neg_binary64_2117 associate-*l/_binary64_2067 associate-*r*_binary64_2064 *-commutative_binary64_2055 sqrt-undiv_binary64_2145 frac-2neg_binary64_2135 clear-num_binary64_2123
Counts
4 → 253
Calls

4 calls:

29.0ms
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))) (*.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))
14.0ms
(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
8.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 10429 to 4551 computations (56.4% saved)

series530.0ms (4.8%)

Error
0.4b
Counts
4 → 53
Calls

4 calls:

132.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
118.0ms
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))) (*.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))
107.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
101.0ms
(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
Compiler

Compiled 3373 to 2840 computations (15.8% saved)

simplify138.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0501310147

prune545.0ms (5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3051306
Fresh088
Picked101
Done011
Total30610316
Error
0.4b
Counts
316 → 10
Compiler

Compiled 10763 to 4953 computations (54% saved)

regimes2.2s (19.7%)

Accuracy

Total 17.4b remaining (98.2%)

Threshold costs 0b (0%)

Compiler

Compiled 17302 to 12723 computations (26.5% saved)

bsearch93.0ms (0.8%)

Steps
ItersRangePoint
9
1.1259252386854316e+126
8.850086950332604e+133
1.0440481246371513e+130
9
6.656901318155849e-295
1.2977753132644072e-289
6.858325427122592e-295
9
-3.3485329400768755e+67
-4.768585116706206e+62
-3.306189866184851e+67
Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068108
168108

end0.0ms (0%)

sample3.2s (28.8%)

Algorithm
1×intervals
Results
501.0ms6040×body128valid
157.0ms644×body2048valid
157.0ms511×body4096valid
79.0ms426×body1024valid
37.0ms246×body512valid
13.0ms133×body256valid
Compiler

Compiled 2414 to 1778 computations (26.3% saved)

Profiling

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