Details

Time bar (total: 14.5s)

analyze130.0ms (0.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.3%)

Algorithm
intervals
Results
12.0ms205×body128valid
7.0ms18×body1024valid
6.0ms256×pre128true
3.0ms17×body512valid
2.0ms15×body256valid
0.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify160.0ms (1.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
22.2b
Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
2.0b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
17.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite91.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64_2130
47×*-un-lft-identity_binary64_2124
25×add-cube-cbrt_binary64_2159 add-sqr-sqrt_binary64_2146
17×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
14×associate-/r/_binary64_2070
11×distribute-lft-out_binary64_2075 flip3-+_binary64_2127 flip-+_binary64_2098
10×associate-/l*_binary64_2069
associate-/l/_binary64_2071
cbrt-undiv_binary64_2158 associate-/r*_binary64_2068 div-inv_binary64_2121 div-exp_binary64_2175
add-log-exp_binary64_2163
frac-times_binary64_2134
flip--_binary64_2099 flip3--_binary64_2128 pow1_binary64_2185
clear-num_binary64_2123 associate-*l/_binary64_2067 prod-exp_binary64_2173 associate-*r/_binary64_2066 cbrt-unprod_binary64_2157 frac-2neg_binary64_2135
sum-log_binary64_2215 +-commutative_binary64_2054
Counts
3 → 111
Calls

3 calls:

35.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
23.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
19.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series726.0ms (5%)

Counts
3 → 9
Calls

3 calls:

351.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
304.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
71.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify111.0ms (0.8%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049415261
149415261

prune253.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1146120
Fresh000
Picked101
Done000
Total1156121
Error
5.3b
Counts
121 → 6
Compiler

Compiled 5229 to 2731 computations (47.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.1b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
4.2b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite158.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
321×times-frac_binary64_2130
290×*-un-lft-identity_binary64_2124
211×add-sqr-sqrt_binary64_2146
140×add-cube-cbrt_binary64_2159
90×associate-*r*_binary64_2064
44×distribute-lft-out_binary64_2075
31×difference-of-squares_binary64_2093 distribute-lft-out--_binary64_2076
26×associate-/l*_binary64_2069
24×associate-/r/_binary64_2070
20×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
15×flip3-+_binary64_2127 flip-+_binary64_2098
12×div-inv_binary64_2121
cbrt-undiv_binary64_2158 associate-/r*_binary64_2068 div-exp_binary64_2175
pow1_binary64_2185 add-log-exp_binary64_2163
associate-*l*_binary64_2065
unswap-sqr_binary64_2092 prod-exp_binary64_2173 div-sub_binary64_2129 associate-/l/_binary64_2071 cbrt-unprod_binary64_2157
clear-num_binary64_2123 associate-*l/_binary64_2067 frac-times_binary64_2134 frac-2neg_binary64_2135
flip--_binary64_2099 pow-prod-down_binary64_2195 flip3--_binary64_2128 sum-log_binary64_2215 *-commutative_binary64_2055 +-commutative_binary64_2054 associate-*r/_binary64_2066
Counts
4 → 295
Calls

4 calls:

43.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
31.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
21.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
16.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series892.0ms (6.2%)

Counts
4 → 12
Calls

4 calls:

362.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
307.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
167.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
55.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify164.0ms (1.1%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0501413438

prune738.0ms (5.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3034307
Fresh235
Picked101
Done000
Total3067313
Error
5.3b
Counts
313 → 7
Compiler

Compiled 14563 to 7677 computations (47.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
0.1b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
1.1b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
4.2b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite170.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
147×times-frac_binary64_2130
137×*-un-lft-identity_binary64_2124
102×add-sqr-sqrt_binary64_2146
90×associate-*r*_binary64_2064
69×add-cube-cbrt_binary64_2159
22×distribute-lft-out_binary64_2075
14×add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
12×difference-of-squares_binary64_2093 distribute-lft-out--_binary64_2076 cbrt-prod_binary64_2155
10×associate-/r/_binary64_2070 flip3-+_binary64_2127 flip-+_binary64_2098
pow1_binary64_2185
unpow-prod-down_binary64_2203 add-log-exp_binary64_2163 cube-prod_binary64_2152
div-inv_binary64_2121
associate-*l*_binary64_2065 cube-div_binary64_2153
cbrt-undiv_binary64_2158 unswap-sqr_binary64_2092 pow-unpow_binary64_2201 prod-exp_binary64_2173 div-exp_binary64_2175 cbrt-unprod_binary64_2157
unpow3_binary64_2190 cbrt-div_binary64_2156 cube-mult_binary64_2154 associate-*l/_binary64_2067 sqr-pow_binary64_2096 frac-times_binary64_2134
pow-prod-down_binary64_2195 pow-pow_binary64_2196 sum-log_binary64_2215 rem-cbrt-cube_binary64_2148 pow-exp_binary64_2192 *-commutative_binary64_2055 pow1/3_binary64_2206 +-commutative_binary64_2054 pow-to-exp_binary64_2193 associate-*r/_binary64_2066 rem-cube-cbrt_binary64_2147
Counts
4 → 176
Calls

4 calls:

45.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
35.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
31.0ms
(pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
30.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series2.1s (14.5%)

Counts
4 → 12
Calls

4 calls:

1.1s
(pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
360.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
344.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
299.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify128.0ms (0.9%)

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
050958304

prune479.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1826188
Fresh246
Picked101
Done000
Total18510195
Error
5.3b
Counts
195 → 10
Compiler

Compiled 9770 to 5461 computations (44.1% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.7b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.2b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
5.9b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite281.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
378×times-frac_binary64_2130
278×*-un-lft-identity_binary64_2124
233×cbrt-prod_binary64_2155
216×associate-*r*_binary64_2064
214×add-sqr-sqrt_binary64_2146
172×add-cube-cbrt_binary64_2159
97×add-exp-log_binary64_2162
55×add-cbrt-cube_binary64_2160
45×prod-exp_binary64_2173 cbrt-unprod_binary64_2157
32×distribute-lft-out_binary64_2075
30×cbrt-undiv_binary64_2158 div-exp_binary64_2175
21×difference-of-squares_binary64_2093 distribute-lft-out--_binary64_2076
16×associate-/r/_binary64_2070
15×flip3-+_binary64_2127 flip-+_binary64_2098
pow1_binary64_2185 associate-*l/_binary64_2067 frac-times_binary64_2134
div-inv_binary64_2121
cbrt-div_binary64_2156 add-log-exp_binary64_2163
pow-prod-down_binary64_2195 associate-*r/_binary64_2066
pow1/3_binary64_2206
sum-log_binary64_2215 *-commutative_binary64_2055 associate-*l*_binary64_2065 +-commutative_binary64_2054
Counts
4 → 313
Calls

4 calls:

98.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
70.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
15.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.0s (7%)

Counts
4 → 12
Calls

4 calls:

374.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
313.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
161.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
160.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify270.0ms (1.9%)

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0499225817
1499225817

prune1.7s (11.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3232325
Fresh279
Picked101
Done000
Total3269335
Error
5.3b
Counts
335 → 9
Compiler

Compiled 26714 to 13971 computations (47.7% saved)

regimes1.4s (9.9%)

Accuracy

Total 1.5b remaining (21%)

Threshold costs 0b (0%)

Compiler

Compiled 26583 to 17121 computations (35.6% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
069114
169114

end0.0ms (0%)

sample3.4s (23.4%)

Algorithm
intervals
Results
412.0ms6490×body128valid
198.0ms8000×pre128true
163.0ms672×body1024valid
93.0ms508×body512valid
35.0ms270×body256valid
19.0ms60×body2048valid
Compiler

Compiled 3850 to 2478 computations (35.6% saved)

Profiling

Loading profile data...