Details

Time bar (total: 2.5min)

analyze122.0ms (0.1%)

Algorithm
1×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)

sample39.0ms (0%)

Algorithm
1×intervals
Results
13.0ms197×body128valid
6.0ms27×body1024valid
6.0ms256×pre128true
3.0ms16×body512valid
2.0ms15×body256valid
0.0ms1×body2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify105.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
0490243
1490243

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 27.8b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0%)

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))
2.4b
(+.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)
22.7b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite98.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
54×times-frac_binary64
47×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
17×add-exp-log_binary64 add-cbrt-cube_binary64
14×associate-/r/_binary64
11×flip3-+_binary64 distribute-lft-out_binary64 flip-+_binary64
10×associate-/l*_binary64
9×associate-/l/_binary64
7×associate-/r*_binary64 cbrt-undiv_binary64 div-inv_binary64 div-exp_binary64
5×add-log-exp_binary64
4×frac-times_binary64
3×pow1_binary64 flip3--_binary64 flip--_binary64
2×cbrt-unprod_binary64 associate-*r/_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 associate-*l/_binary64
1×+-commutative_binary64 sum-log_binary64
Counts
3 → 111
Calls

3 calls:

41.0ms
(+.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)
24.0ms
(/.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))
17.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (1%)

Counts
3 → 9
Calls

3 calls:

694.0ms
(+.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)
602.0ms
(/.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))
139.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify103.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049355261
149355261

prune852.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh000
Picked101
Done000
Total11110121

Merged error: 7.3b

Counts
121 → 10
Compiler

Compiled 21347 to 12894 computations (39.6% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.4b
(*.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)))))
4.8b
(+.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)

rewrite175.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
321×times-frac_binary64
290×*-un-lft-identity_binary64
211×add-sqr-sqrt_binary64
140×add-cube-cbrt_binary64
90×associate-*r*_binary64
44×distribute-lft-out_binary64
31×difference-of-squares_binary64 distribute-lft-out--_binary64
26×associate-/l*_binary64
24×associate-/r/_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
15×flip3-+_binary64 flip-+_binary64
12×div-inv_binary64
7×associate-/r*_binary64 cbrt-undiv_binary64 div-exp_binary64
6×add-log-exp_binary64 pow1_binary64
4×associate-*l*_binary64
3×associate-/l/_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 div-sub_binary64 prod-exp_binary64
2×clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 flip3--_binary64 associate-*r/_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 295
Calls

4 calls:

52.0ms
(*.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)
23.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (1.1%)

Counts
4 → 12
Calls

4 calls:

708.0ms
(+.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)
574.0ms
(*.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)))))
315.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
112.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify161.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0497013438
1497013438

prune1.0s (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3016307
Fresh459
Picked011
Done000
Total30512317

Merged error: 7.3b

Counts
317 → 12
Compiler

Compiled 21080 to 11781 computations (44.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(exp.f64 (log.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)))
1.4b
(*.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)))))
3.2b
(log.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))
4.8b
(+.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)

rewrite183.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
147×times-frac_binary64
134×*-un-lft-identity_binary64
99×add-sqr-sqrt_binary64
90×associate-*r*_binary64
66×add-cube-cbrt_binary64
22×distribute-lft-out_binary64
14×add-exp-log_binary64
13×add-cbrt-cube_binary64
12×difference-of-squares_binary64 distribute-lft-out--_binary64
10×flip3-+_binary64 associate-/r/_binary64 flip-+_binary64
8×pow1_binary64
6×add-log-exp_binary64 log-prod_binary64
5×div-inv_binary64
4×associate-*l*_binary64 log-div_binary64 exp-prod_binary64
3×cbrt-unprod_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 exp-sum_binary64 prod-exp_binary64 div-exp_binary64
2×log-pow_binary64 exp-diff_binary64 frac-times_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 rem-log-exp_binary64 associate-*r/_binary64 rem-exp-log_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 159
Calls

4 calls:

52.0ms
(*.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)))))
33.0ms
(exp.f64 (log.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)))
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)
31.0ms
(log.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))

series4.6s (3.1%)

Counts
4 → 12
Calls

4 calls:

2.1s
(log.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))
1.2s
(exp.f64 (log.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)))
700.0ms
(+.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)
592.0ms
(*.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)))))

simplify108.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
051237173

prune630.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1647171
Fresh6410
Picked101
Done011
Total17112183

Merged error: 4.5b

Counts
183 → 12
Compiler

Compiled 15147 to 8857 computations (41.5% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

1.4b
(*.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)))))
3.2b
(log.f64 (/.f64 (+.f64 1 (pow.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))))) 3)) (+.f64 1 (*.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))))) (-.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)))))
3.4b
(-.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)
4.8b
(+.f64 1 (pow.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))))) 3))

rewrite161.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
159×times-frac_binary64
148×*-un-lft-identity_binary64
105×add-sqr-sqrt_binary64
90×associate-*r*_binary64
72×add-cube-cbrt_binary64
26×distribute-lft-out_binary64
18×log-prod_binary64
16×add-exp-log_binary64
13×add-cbrt-cube_binary64
12×associate-/r/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
9×flip3-+_binary64 flip-+_binary64
8×add-log-exp_binary64
7×pow1_binary64
6×div-inv_binary64
4×associate-*l*_binary64 div-exp_binary64
3×cbrt-unprod_binary64 cbrt-undiv_binary64 cancel-sign-sub-inv_binary64 unswap-sqr_binary64 prod-exp_binary64
2×rem-log-exp_binary64 frac-times_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 associate-*r/_binary64 log-pow_binary64 log-div_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 172
Calls

4 calls:

52.0ms
(*.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)))))
34.0ms
(-.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)
10.0ms
(log.f64 (/.f64 (+.f64 1 (pow.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))))) 3)) (+.f64 1 (*.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))))) (-.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)))))
7.0ms
(+.f64 1 (pow.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))))) 3))

series2.3min (92.3%)

Calls

2 calls:

36.4s
(+.f64 1 (pow.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))))) 3))
407.0ms
(-.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)

Profiling

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