Details

Time bar (total: 2.5min)

analyze35.2s (23.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
0%99.8%0.2%11
0%99.8%0.2%12
0%99.8%0.2%13
0%99.8%0.2%14
Compiler

Compiled 184 to 125 computations (32.1% saved)

sample4.8s (3.2%)

Algorithm
intervals
Results
2.0s105×body4096valid
1.9s56×body8192valid
632.0ms61×body2048valid
163.0ms25×body1024valid
25.0msbody512valid
12.0msbody1024invalid
8.0msbody256valid
Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify208.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05065287

prune46.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 64.0b

Counts
2 → 1
Compiler

Compiled 360 to 236 computations (34.4% saved)

localize139.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.3b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.3b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.3b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
36.7b
(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 x-scale y-scale)) 2))))

rewrite641.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
add-log-exp_binary64 cancel-sign-sub-inv_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64 frac-sub_binary64 sqrt-div_binary64
flip3-+_binary64 flip-+_binary64
pow1_binary64 distribute-lft-out_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 unpow-prod-down_binary64
distribute-lft-out--_binary64
diff-log_binary64 frac-add_binary64 difference-of-squares_binary64
sub-neg_binary64 flip3--_binary64 flip--_binary64 associate--l+_binary64 sum-log_binary64
Counts
4 → 53
Calls

4 calls:

560.0ms
(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 x-scale y-scale)) 2))))
5.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

series21.1s (14.1%)

Counts
4 → 12
Calls

4 calls:

21.0s
(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) PI.f64)) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 x-scale y-scale)) 2))))
24.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
22.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
19.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify259.0ms (0.2%)

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
0497111862
1497111862

prune1.4s (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New63265
Fresh000
Picked101
Done000
Total64266

Merged error: 59.8b

Counts
66 → 2
Compiler

Compiled 15116 to 9059 computations (40.1% saved)

localize45.0ms (0%)

Local error

Found 4 expressions with local error:

16.6b
(*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0)
17.8b
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
17.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
20.3b
(*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))

rewrite423.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
1300×add-exp-log_binary64
997×prod-exp_binary64
526×add-cbrt-cube_binary64
400×cbrt-unprod_binary64
250×pow1_binary64
205×pow-prod-down_binary64
145×div-exp_binary64
72×pow-exp_binary64
40×cbrt-undiv_binary64
36×pow-to-exp_binary64
14×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64 associate-*r*_binary64 add-cube-cbrt_binary64 associate-*l*_binary64
distribute-rgt-neg-out_binary64 times-frac_binary64
associate-*l/_binary64
add-log-exp_binary64 associate-/l*_binary64
distribute-lft-neg-out_binary64 unswap-sqr_binary64 sqrt-prod_binary64 *-commutative_binary64
unpow2_binary64 sqr-pow_binary64 div-inv_binary64
associate-/l/_binary64 associate-/r*_binary64 mul0-rgt_binary64 clear-num_binary64 unpow-prod-down_binary64 frac-2neg_binary64 sqrt-div_binary64
Counts
4 → 386
Calls

4 calls:

77.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
64.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
59.0ms
(*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))
21.0ms
(*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0)

series54.0ms (0%)

Counts
4 → 12
Calls

4 calls:

19.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
17.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
12.0ms
(*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0))
5.0ms
(*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) 0)

simplify285.0ms (0.2%)

Algorithm
egg-herbie
Counts
398 → 398
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
047012605
147012605

prune860.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3971398
Fresh011
Picked101
Done000
Total3982400

Merged error: 40.8b

Counts
400 → 2
Compiler

Compiled 9460 to 4312 computations (54.4% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify12.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

prune5.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done000
Total022

Merged error: 40.8b

Counts
2 → 2
Compiler

Compiled 53 to 29 computations (45.3% saved)

localize54.0ms (0%)

Local error

Found 4 expressions with local error:

14.0b
(*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
15.1b
(/.f64 (*.f64 a a) (*.f64 y-scale y-scale))
31.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
33.1b
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))

rewrite325.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
244×add-exp-log_binary64
144×prod-exp_binary64
100×add-cbrt-cube_binary64
52×cbrt-unprod_binary64
49×div-exp_binary64
30×associate-*l*_binary64
27×times-frac_binary64
23×add-sqr-sqrt_binary64
22×pow1_binary64 pow-exp_binary64
19×*-un-lft-identity_binary64 cbrt-undiv_binary64 add-cube-cbrt_binary64
13×pow-prod-down_binary64
11×pow-to-exp_binary64
associate-*r*_binary64
unpow2_binary64 associate-*r/_binary64 sqr-pow_binary64 associate-/l*_binary64 associate-*l/_binary64
add-log-exp_binary64 unpow-prod-down_binary64 div-inv_binary64
associate-/l/_binary64 distribute-rgt-neg-out_binary64 unswap-sqr_binary64 sqrt-prod_binary64 sqrt-div_binary64
associate-/r*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
frac-times_binary64
Counts
4 → 182
Calls

4 calls:

105.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
91.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
31.0ms
(*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
13.0ms
(/.f64 (*.f64 a a) (*.f64 y-scale y-scale))

series420.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

234.0ms
(*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
97.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))
54.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 8 (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (*.f64 2 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
34.0ms
(/.f64 (*.f64 a a) (*.f64 y-scale y-scale))

simplify210.0ms (0.1%)

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049647256
149647256

prune679.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1877194
Fresh000
Picked101
Done011
Total1888196

Merged error: 34.0b

Counts
196 → 8
Compiler

Compiled 10432 to 3933 computations (62.3% saved)

regimes1.8s (1.2%)

Compiler

Compiled 14560 to 8890 computations (38.9% saved)

bsearch4.0s (2.7%)

Steps
ItersRangePoint
6
1.1924540025417866e+87
1.3681706298322213e+88
4.800894394302007e+87
9
-3.028737428679318e-71
-9.185510969988598e-77
-5.245877687206303e-74
Compiler

Compiled 1 to 5 computations (-400% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02325
12325

end0.0ms (0%)

sample1.3min (51.3%)

Algorithm
intervals
Results
33.2s1971×body4096valid
29.9s851×body8192valid
9.9s967×body2048valid
2.3s359×body1024valid
470.0ms110×body512valid
188.0ms16×body2048invalid
161.0ms58×body256valid
89.0ms13×body1024invalid
28.0msbody512invalid
27.0ms21×body128valid
5.0msbody256invalid
1.0msbody128invalid
Compiler

Compiled 184 to 130 computations (29.3% saved)

Profiling

Loading profile data...