Details

Time bar (total: 39.1s)

analyze128.0ms (0.3%)

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)

sample41.0ms (0.1%)

Algorithm
intervals
Results
12.0ms205×body80valid
7.0ms15×body1280valid
6.0ms256×pre80true
3.0ms14×body640valid
2.0ms14×body320valid
1.0msbody160valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify120.0ms (0.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
0530043

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 22.9b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 alpha beta) (*.f64 2 i))
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))
2.1b
(+.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)
18.3b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite104.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64
48×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
14×associate-/r/_binary64
12×flip3-+_binary64 flip-+_binary64
11×add-log-exp_binary64 distribute-lft-out_binary64
10×associate-/l*_binary64
associate-/l/_binary64
associate-/r*_binary64 cbrt-undiv_binary64 div-inv_binary64 div-exp_binary64
pow1_binary64 insert-posit16 frac-times_binary64 sum-log_binary64
flip3--_binary64 flip--_binary64
cbrt-unprod_binary64 associate-*r/_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 +-commutative_binary64 associate-*l/_binary64
associate-+l+_binary64
Counts
4 → 128
Calls

4 calls:

44.0ms
(+.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)
28.0ms
(/.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)))
8.0ms
(+.f64 (+.f64 alpha beta) (*.f64 2 i))

series1.4s (3.5%)

Counts
4 → 12
Calls

4 calls:

651.0ms
(+.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)
558.0ms
(/.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))
129.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
29.0ms
(+.f64 (+.f64 alpha beta) (*.f64 2 i))

simplify108.0ms (0.3%)

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
051595608

prune287.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New12911140
Fresh000
Picked101
Done000
Total13011141

Merged error: 4.5b

Counts
141 → 11
Compiler

Compiled 6053 to 3181 computations (47.4% 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 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
2.1b
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite109.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity_binary64
45×add-sqr-sqrt_binary64
35×times-frac_binary64
26×add-cube-cbrt_binary64
21×associate-*r*_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
flip3-+_binary64 flip-+_binary64
associate-/l/_binary64 associate-/r*_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
add-log-exp_binary64 pow1_binary64 cbrt-undiv_binary64 associate-/r/_binary64 associate-/l*_binary64 div-exp_binary64
cbrt-unprod_binary64 distribute-lft-out_binary64 associate-*l*_binary64 prod-exp_binary64 insert-posit16 frac-times_binary64 associate-*l/_binary64
div-inv_binary64
associate-*r/_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64
pow-prod-down_binary64 flip3--_binary64 div-sub_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 133
Calls

4 calls:

32.0ms
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
31.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
22.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
14.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.5s (3.7%)

Counts
4 → 12
Calls

4 calls:

649.0ms
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
556.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
127.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
119.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify97.0ms (0.2%)

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
052894346

prune236.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1432145
Fresh3710
Picked101
Done000
Total1479156

Merged error: 4.5b

Counts
156 → 9
Compiler

Compiled 5793 to 3078 computations (46.9% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.4b
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite294.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
603×times-frac_binary64
484×*-un-lft-identity_binary64
408×add-sqr-sqrt_binary64
260×add-cube-cbrt_binary64
219×sqrt-prod_binary64
153×associate-*r*_binary64
67×distribute-lft-out_binary64
45×difference-of-squares_binary64 distribute-lft-out--_binary64
38×associate-/r/_binary64
34×associate-*l*_binary64
32×add-exp-log_binary64 add-cbrt-cube_binary64
25×associate-/l*_binary64
21×flip3-+_binary64 flip-+_binary64
19×div-inv_binary64
15×unswap-sqr_binary64
14×associate-/r*_binary64
13×cbrt-undiv_binary64 div-exp_binary64
sqrt-div_binary64
add-log-exp_binary64 pow1_binary64 cbrt-unprod_binary64 prod-exp_binary64
insert-posit16
associate-/l/_binary64
div-sub_binary64 clear-num_binary64 frac-2neg_binary64
pow-prod-down_binary64 associate-*r/_binary64 +-commutative_binary64 frac-times_binary64 associate-*l/_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 489
Calls

4 calls:

142.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
56.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
28.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
17.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.8s (4.7%)

Counts
4 → 12
Calls

4 calls:

640.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
554.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
343.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
283.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify290.0ms (0.7%)

Algorithm
egg-herbie
Counts
501 → 501
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
0537027830

prune2.2s (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4992501
Fresh268
Picked011
Done000
Total5019510

Merged error: 4.5b

Counts
510 → 9
Compiler

Compiled 30221 to 16883 computations (44.1% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.6b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
5.9b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite1.0s (2.6%)

Algorithm
rewrite-expression-head
Rules
6211×times-frac_binary64
4294×*-un-lft-identity_binary64
3048×add-sqr-sqrt_binary64
2585×sqrt-prod_binary64
2326×add-cube-cbrt_binary64
1077×associate-*r*_binary64
645×distribute-lft-out_binary64
339×difference-of-squares_binary64 distribute-lft-out--_binary64
262×associate-/r/_binary64
174×associate-/l*_binary64
134×flip3-+_binary64 flip-+_binary64
131×div-inv_binary64
36×sqrt-div_binary64
32×add-exp-log_binary64 add-cbrt-cube_binary64
15×cbrt-undiv_binary64 div-exp_binary64
14×associate-/r*_binary64
11×unswap-sqr_binary64
add-log-exp_binary64 pow1_binary64
div-sub_binary64
cbrt-unprod_binary64 associate-*l*_binary64 prod-exp_binary64 insert-posit16
associate-/l/_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64
pow-prod-down_binary64 associate-*r/_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 2573
Calls

4 calls:

352.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
135.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
92.0ms
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.8s (4.7%)

Counts
4 → 12
Calls

4 calls:

630.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
554.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
347.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
309.0ms
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify1.4s (3.6%)

Algorithm
egg-herbie
Counts
2585 → 2585
Iterations

Useful iterations: 0 (119.0ms)

IterNodesCost
05535178919

prune24.4s (62.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New258412585
Fresh077
Picked011
Done011
Total2584102594

Merged error: 4.5b

Counts
2594 → 10
Compiler

Compiled 179449 to 101716 computations (43.3% saved)

regimes145.0ms (0.4%)

Compiler

Compiled 1444 to 1004 computations (30.5% saved)

bsearch100.0ms (0.3%)

Steps
ItersRangePoint
9
2.4117717576352263e+127
2.646547745325264e+134
8.457234180095517e+129
9
1.3386321286407027e+73
6.861209131634704e+81
2.1817558498141728e+73
4
6.778926584227262e+26
1.0209553910028353e+27
7.958204727471386e+26
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
084146
184146

end0.0ms (0%)

sample1.5s (3.7%)

Algorithm
intervals
Results
369.0ms6402×body80valid
197.0ms8000×pre80true
141.0ms506×body1280valid
125.0ms554×body640valid
56.0ms349×body320valid
21.0ms189×body160valid
Compiler

Compiled 494 to 337 computations (31.8% saved)

Profiling

Loading profile data...