Details

Time bar (total: 9.0s)

analyze591.0ms (6.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample43.0ms (0.5%)

Algorithm
intervals
Results
10.0ms164×body128valid
8.0ms42×body2048valid
4.0ms15×body4096valid
3.0ms19×body1024valid
1.0ms12×body512valid
1.0ms22×body128nan
0.0msbody128invalid
0.0msbody256valid
Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify170.0ms (1.9%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
071420
171420

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
37.0b
Counts
2 → 1
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.3b
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
0.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
0.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
0.3b
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite48.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
21×times-frac_binary64
19×add-cube-cbrt_binary64
11×sqrt-prod_binary64
10×add-log-exp_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
cancel-sign-sub-inv_binary64 associate-/l*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64 distribute-rgt-neg-in_binary64
flip3--_binary64 flip--_binary64
associate-/r*_binary64 diff-log_binary64
associate-/l/_binary64 sub-neg_binary64 sqrt-div_binary64
pow1/2_binary64 associate--l-_binary64 neg-sub0_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 neg-log_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 96
Calls

8 calls:

12.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
11.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
10.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
0.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)

series545.0ms (6.1%)

Counts
4 → 67
Calls

4 calls:

166.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
128.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
127.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
123.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 1637 to 1341 computations (18.1% saved)

simplify80.0ms (0.9%)

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049703346
149703346

prune183.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1549163
Fresh000
Picked101
Done000
Total1559164
Error
7.4b
Counts
164 → 9
Compiler

Compiled 3054 to 607 computations (80.1% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

12.2b
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
5.0b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
5.0b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.2b
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite51.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64
58×add-sqr-sqrt_binary64
43×*-un-lft-identity_binary64
29×add-cube-cbrt_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
14×difference-of-squares_binary64
13×associate-/l*_binary64
10×associate-/r/_binary64 sqrt-prod_binary64
associate-/r*_binary64
flip3--_binary64 cbrt-undiv_binary64 distribute-lft-out--_binary64 div-exp_binary64 flip--_binary64
add-log-exp_binary64 div-inv_binary64
pow1_binary64
cancel-sign-sub-inv_binary64
cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 sqrt-div_binary64
associate-/l/_binary64 sub-neg_binary64 pow1/2_binary64 diff-log_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
Counts
4 → 129
Calls

8 calls:

14.0ms
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0ms
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
10.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
0.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

series732.0ms (8.2%)

Counts
4 → 69
Calls

4 calls:

243.0ms
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
209.0ms
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
144.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
136.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 2333 to 1676 computations (28.2% saved)

simplify107.0ms (1.2%)

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049505148
149505148

prune153.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1971198
Fresh178
Picked101
Done000
Total1998207
Error
7.4b
Counts
207 → 8
Compiler

Compiled 4614 to 856 computations (81.4% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.1b
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
0.1b
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite33.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
18×times-frac_binary64
17×add-cube-cbrt_binary64
10×difference-of-squares_binary64
add-log-exp_binary64 sqrt-prod_binary64
associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64 distribute-lft-out--_binary64
flip3--_binary64 cancel-sign-sub-inv_binary64 flip--_binary64
associate-/l*_binary64
sub-neg_binary64 diff-log_binary64 associate-/r/_binary64 sqrt-div_binary64
pow1/2_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 85
Calls

8 calls:

10.0ms
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.0ms
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))

series618.0ms (6.9%)

Counts
4 → 71
Calls

4 calls:

209.0ms
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
144.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
140.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
124.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 2065 to 1671 computations (19.1% saved)

simplify54.0ms (0.6%)

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
051253119

prune128.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1533156
Fresh347
Picked011
Done000
Total1568164
Error
7.4b
Counts
164 → 8
Compiler

Compiled 3136 to 928 computations (70.4% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.2b
(*.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
0.1b
(/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
0.2b
(*.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
25.6b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite42.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
26×*-un-lft-identity_binary64
24×associate-*r*_binary64
20×times-frac_binary64
17×add-cube-cbrt_binary64
13×add-exp-log_binary64
add-cbrt-cube_binary64
add-log-exp_binary64 difference-of-squares_binary64
pow1_binary64 sqrt-prod_binary64
flip3--_binary64 cancel-sign-sub-inv_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip--_binary64
associate-*l*_binary64 unswap-sqr_binary64
sub-neg_binary64 diff-log_binary64 cbrt-unprod_binary64 associate-/r/_binary64 div-exp_binary64 sqrt-div_binary64
pow-prod-down_binary64 pow1/2_binary64 1-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 rec-exp_binary64 un-div-inv_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 91
Calls

8 calls:

16.0ms
(*.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
0.0ms
(/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))

series619.0ms (6.9%)

Counts
4 → 71
Calls

4 calls:

211.0ms
(*.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
147.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
134.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
127.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 2225 to 1831 computations (17.7% saved)

simplify68.0ms (0.8%)

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052782888

prune132.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1611162
Fresh066
Picked011
Done011
Total1619170
Error
7.4b
Counts
170 → 9
Compiler

Compiled 3396 to 1211 computations (64.3% saved)

simplify79.0ms (0.9%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
018841386
118841386

regimes744.0ms (8.3%)

Compiler

Compiled 2682 to 1743 computations (35% saved)

bsearch82.0ms (0.9%)

Steps
ItersRangePoint
8
1.6621865169664383e+118
5.129650521579702e+120
4.5829281059216323e+120
6
8.963326552883708e-271
8.197791807140359e-270
1.0584144284358635e-270
9
-1.0451269989421558e+143
-1.1049780562537373e+138
-1.344663677076728e+139
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes325.0ms (3.6%)

Compiler

Compiled 696 to 657 computations (5.6% saved)

bsearch81.0ms (0.9%)

Steps
ItersRangePoint
8
1.6621865169664383e+118
5.129650521579702e+120
3.741676379449926e+119
6
8.963326552883708e-271
8.197791807140359e-270
9.316977997537944e-271
9
-1.0451269989421558e+143
-1.1049780562537373e+138
-2.4309328711269665e+140
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes222.0ms (2.5%)

Compiler

Compiled 486 to 492 computations (-1.2% saved)

bsearch60.0ms (0.7%)

Steps
ItersRangePoint
6
1.6767930608218287e-74
2.0526380419239506e-73
2.125184487670011e-74
9
-1.0451269989421558e+143
-1.1049780562537373e+138
-5.126738915237279e+141
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes188.0ms (2.1%)

Compiler

Compiled 411 to 438 computations (-6.6% saved)

bsearch54.0ms (0.6%)

Steps
ItersRangePoint
6
1.6767930608218287e-74
2.0526380419239506e-73
1.3605056567740671e-73
11
-5.1328883408937556e-130
-1.494813238907461e-149
-5.075747447679184e-130
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes164.0ms (1.8%)

Compiler

Compiled 315 to 357 computations (-13.3% saved)

bsearch51.0ms (0.6%)

Steps
ItersRangePoint
6
1.6767930608218287e-74
2.0526380419239506e-73
4.445877257385786e-74
9
-4.1544417763086953e-101
-4.9026669614985984e-107
-2.3523495507255537e-104
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes145.0ms (1.6%)

Compiler

Compiled 261 to 306 computations (-17.2% saved)

bsearch53.0ms (0.6%)

Steps
ItersRangePoint
6
1.6767930608218287e-74
2.0526380419239506e-73
1.203331638996701e-73
11
-5.1328883408937556e-130
-1.494813238907461e-149
-1.825261055624557e-132
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes107.0ms (1.2%)

Compiler

Compiled 216 to 261 computations (-20.8% saved)

bsearch34.0ms (0.4%)

Steps
ItersRangePoint
10
-5.3319334640310345e-190
-4.814717761641575e-200
-4.8572594842978696e-200
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes69.0ms (0.8%)

Compiler

Compiled 60 to 105 computations (-75% saved)

bsearch32.0ms (0.4%)

Steps
ItersRangePoint
10
-5.3319334640310345e-190
-4.814717761641575e-200
-4.8572594842978696e-200
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes28.0ms (0.3%)

Compiler

Compiled 30 to 72 computations (-140% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.3%)

Accuracy

Total 1.1b remaining (16.4%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch12.0ms (0.1%)

Compiler

Compiled 265 to 189 computations (28.7% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0180391
1180391

end0.0ms (0%)

sample2.0s (21.9%)

Algorithm
intervals
Results
232.0ms1156×body2048valid
224.0ms5176×body128valid
111.0ms710×body1024valid
104.0ms417×body4096valid
43.0ms350×body512valid
29.0ms750×body128nan
15.0ms191×body256valid
11.0ms264×body128invalid
Compiler

Compiled 1171 to 778 computations (33.6% saved)

Pareto

0.5470372843967185

Profiling

Loading profile data...