Details

Time bar (total: 3.6s)

analyze44.0ms (1.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14

sample34.0ms (0.9%)

Algorithm
1×intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify32.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0523053

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 55.2b

Counts
2 → 1

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
0.1b
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
34.3b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))
47.2b
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))

rewrite105.0ms (2.9%)

Algorithm
1×rewrite-expression-head
Rules
61×add-exp-log_binary64 add-cbrt-cube_binary64
58×times-frac_binary64
54×flip3-+_binary64 flip-+_binary64
50×associate-/r/_binary64
44×add-sqr-sqrt_binary64
36×frac-times_binary64
30×associate-*r/_binary64
28×*-un-lft-identity_binary64 add-cube-cbrt_binary64
22×cbrt-unprod_binary64 prod-exp_binary64
19×cbrt-undiv_binary64 div-exp_binary64
18×associate-*l/_binary64
16×pow1_binary64
14×difference-of-squares_binary64 associate-/l*_binary64
9×associate-/l/_binary64
7×div-inv_binary64
6×associate-*r*_binary64
5×associate-/r*_binary64
4×pow-prod-down_binary64 add-log-exp_binary64 associate-*l*_binary64
3×swap-sqr_binary64
2×distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×flip3--_binary64 pow-prod-up_binary64 pow-plus_binary64 unswap-sqr_binary64 pow-sqr_binary64 flip--_binary64 pow2_binary64
Counts
4 → 200
Calls

4 calls:

40.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))
27.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))
15.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))

series562.0ms (15.5%)

Counts
4 → 12
Calls

4 calls:

440.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))
74.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))
32.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
17.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))

simplify85.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0499910097
1499910097

prune499.0ms (13.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2075212
Fresh000
Picked101
Done000
Total2085213

Merged error: 33.4b

Counts
213 → 5

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
33.7b
(/.f64 (*.f64 (*.f64 i i) 0.25) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))

rewrite36.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
13×add-exp-log_binary64 add-cbrt-cube_binary64
12×add-sqr-sqrt_binary64
9×pow1_binary64
8×*-un-lft-identity_binary64 add-cube-cbrt_binary64
6×flip3-+_binary64 flip-+_binary64
4×associate-/r*_binary64 cbrt-unprod_binary64 prod-exp_binary64 times-frac_binary64 frac-times_binary64
3×swap-sqr_binary64 associate-*r*_binary64 cbrt-undiv_binary64 associate-*l*_binary64 div-exp_binary64
2×add-log-exp_binary64 associate-*r/_binary64 associate-/r/_binary64 difference-of-squares_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 flip3--_binary64 pow-prod-up_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 pow-plus_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 pow-sqr_binary64 flip--_binary64 pow2_binary64 *-commutative_binary64
Counts
2 → 62
Calls

2 calls:

20.0ms
(/.f64 (*.f64 (*.f64 i i) 0.25) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))
13.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))

series77.0ms (2.1%)

Counts
2 → 6
Calls

2 calls:

62.0ms
(/.f64 (*.f64 (*.f64 i i) 0.25) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))) 1.0))
15.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))

simplify29.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
051211188

prune108.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh044
Picked101
Done000
Total66773

Merged error: 33.3b

Counts
73 → 7

localize16.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.1b
(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
29.8b
(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))

rewrite37.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
21×add-exp-log_binary64 add-cbrt-cube_binary64
14×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
10×associate-/r*_binary64 times-frac_binary64
8×cbrt-undiv_binary64 div-exp_binary64
6×add-cube-cbrt_binary64
5×cbrt-unprod_binary64 prod-exp_binary64
4×associate-/r/_binary64 difference-of-squares_binary64
2×add-log-exp_binary64 pow1_binary64 distribute-lft-out_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 distribute-lft-out--_binary64 div-inv_binary64 sqrt-prod_binary64
1×flip3-+_binary64 associate-/l/_binary64 flip3--_binary64 flip--_binary64 flip-+_binary64 associate-*l/_binary64
Counts
2 → 59
Calls

2 calls:

23.0ms
(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
12.0ms
(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))

series106.0ms (2.9%)

Counts
2 → 6
Calls

2 calls:

74.0ms
(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
31.0ms
(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))

simplify64.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049771396
149771396

prune128.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New60565
Fresh246
Picked101
Done000
Total63972

Merged error: 7.3b

Counts
72 → 9

localize14.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))
0.1b
(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
0.1b
(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))))

rewrite54.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Rules
41×*-un-lft-identity_binary64
36×add-sqr-sqrt_binary64
31×times-frac_binary64
24×add-exp-log_binary64 add-cbrt-cube_binary64
23×add-cube-cbrt_binary64
18×associate-*r*_binary64
10×associate-/r*_binary64
7×cbrt-unprod_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
6×associate-/r/_binary64
5×pow1_binary64
4×difference-of-squares_binary64 associate-/l*_binary64
3×add-log-exp_binary64 associate-*l*_binary64 div-inv_binary64
2×flip3-+_binary64 associate-*r/_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 distribute-lft-out--_binary64 sqrt-prod_binary64 flip-+_binary64
1×pow-prod-down_binary64 associate-/l/_binary64 flip3--_binary64 flip--_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
3 → 104
Calls

3 calls:

23.0ms
(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
15.0ms
(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))))
10.0ms
(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))

series110.0ms (3%)

Counts
3 → 9
Calls

3 calls:

64.0ms
(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))) 0.25) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) (sqrt.f64 1.0)))
23.0ms
(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0))))
23.0ms
(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)) (sqrt.f64 1.0)))

simplify34.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
053902131

prune196.0ms (5.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1067113
Fresh268
Picked101
Done000
Total10913122

Merged error: 7.3b

Counts
122 → 13

regimes257.0ms (7.1%)

Accuracy

Total 4.1b remaining (35.7%)

Threshold costs 0b (0%)

bsearch11.0ms (0.3%)

Steps
ItersRangePoint
4
2.316113881829469e+49
4.324400894895351e+49
4.260945402677668e+49

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05190
15190

end0.0ms (0%)

sample954.0ms (26.3%)

Algorithm
1×intervals
Results
609.0ms8000×body80valid
170.0ms8000×pre80true

Profiling

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