Details

Time bar (total: 7.8s)

analyze789.0ms (10.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14
Compiler

Compiled 22 to 18 computations (18.2% saved)

sample43.0ms (0.6%)

Algorithm
intervals
Results
13.0ms192×body128valid
7.0ms25×body2048valid
5.0ms256×pre128true
3.0ms17×body1024valid
2.0msbody4096valid
1.0msbody256valid
1.0msbody512valid
Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify96.0ms (1.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03826
13826

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
13.6b
Counts
2 → 1
Compiler

Compiled 34 to 28 computations (17.6% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.9b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
0.0b
(+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
0.9b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
14.5b
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

rewrite48.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64_3147
21×add-sqr-sqrt_binary64_3169
20×add-cube-cbrt_binary64_3182
18×times-frac_binary64_3153
16×sqrt-prod_binary64_3163
pow1_binary64_3208
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 associate-/r*_binary64_3091 add-log-exp_binary64_3186 sqrt-div_binary64_3164
flip-+_binary64_3121 flip3-+_binary64_3150
sqrt-pow1_binary64_3165 associate-/l*_binary64_3092
pow1/2_binary64_3227 associate-/r/_binary64_3093 associate-*r/_binary64_3089
clear-num_binary64_3146 pow-prod-down_binary64_3218 frac-2neg_binary64_3158 distribute-lft-out_binary64_3098 rem-sqrt-square_binary64_3160 +-commutative_binary64_3077 cbrt-undiv_binary64_3181 div-exp_binary64_3198 div-inv_binary64_3144 sum-log_binary64_3238
Counts
4 → 81
Calls

8 calls:

14.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
13.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
8.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))
0.0ms
(+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))

series552.0ms (7.1%)

Counts
4 → 54
Calls

4 calls:

178.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
135.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
122.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
116.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))
Compiler

Compiled 1498 to 1382 computations (7.7% saved)

simplify62.0ms (0.8%)

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050243051

prune252.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1296135
Fresh000
Picked101
Done000
Total1306136
Error
2.7b
Counts
136 → 6
Compiler

Compiled 3092 to 2046 computations (33.8% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))))
0.0b
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
0.0b
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))
0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))))
0.2b
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
2.6b
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
14.5b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite37.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64_3169
24×associate-*r*_binary64_3087
22×times-frac_binary64_3153
21×*-un-lft-identity_binary64_3147
19×add-cube-cbrt_binary64_3182
15×sqrt-prod_binary64_3163
13×add-exp-log_binary64_3185
10×pow1_binary64_3208
add-cbrt-cube_binary64_3183
add-log-exp_binary64_3186 sqrt-div_binary64_3164
unswap-sqr_binary64_3115
flip-+_binary64_3121 flip3-+_binary64_3150 prod-exp_binary64_3196
sqrt-pow1_binary64_3165 associate-*l*_binary64_3088 associate-*r/_binary64_3089
pow-prod-down_binary64_3218 pow1/2_binary64_3227 cbrt-unprod_binary64_3180 div-exp_binary64_3198 associate-/r/_binary64_3093
*-commutative_binary64_3078 rem-sqrt-square_binary64_3160 +-commutative_binary64_3077 cbrt-undiv_binary64_3181 un-div-inv_binary64_3145 1-exp_binary64_3191 rec-exp_binary64_3197 div-inv_binary64_3144 sum-log_binary64_3238
Counts
4 → 88
Calls

8 calls:

15.0ms
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
5.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
4.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))))
3.0ms
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
0.0ms
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))

series554.0ms (7.1%)

Counts
4 → 54
Calls

4 calls:

175.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))))
140.0ms
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
124.0ms
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
114.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
Compiler

Compiled 1542 to 1426 computations (7.5% saved)

simplify58.0ms (0.7%)

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
049662903
149662903

prune173.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1420142
Fresh055
Picked011
Done000
Total1426148
Error
2.7b
Counts
148 → 6
Compiler

Compiled 3362 to 2306 computations (31.4% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (*.f64 1/2 (/.f64 (-.f64 1 (/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))
0.0b
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
0.0b
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
1.0b
(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
1.9b
(-.f64 1 (/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))
3.1b
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
14.5b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite57.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64_3169
33×cancel-sign-sub-inv_binary64_3113
31×*-un-lft-identity_binary64_3147
30×times-frac_binary64_3153
22×add-cube-cbrt_binary64_3182
14×sqrt-prod_binary64_3163
10×difference-of-squares_binary64_3116
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183
add-log-exp_binary64_3186
associate-/r/_binary64_3093
pow1_binary64_3208
flip-+_binary64_3121 flip3-+_binary64_3150 sqrt-div_binary64_3164
associate-/r*_binary64_3091 div-inv_binary64_3144
flip--_binary64_3122 flip3--_binary64_3151 sub-neg_binary64_3140 distribute-lft-out--_binary64_3099 cbrt-undiv_binary64_3181 div-exp_binary64_3198 diff-log_binary64_3239
clear-num_binary64_3146 frac-2neg_binary64_3158 rem-sqrt-square_binary64_3160 prod-exp_binary64_3196 sqrt-pow1_binary64_3165 pow1/2_binary64_3227 cbrt-unprod_binary64_3180 associate-/l*_binary64_3092
Counts
4 → 105
Calls

8 calls:

15.0ms
(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
11.0ms
(-.f64 1 (/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))
9.0ms
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
5.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
0.0ms
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))

series618.0ms (7.9%)

Counts
4 → 62
Calls

4 calls:

213.0ms
(-.f64 1 (/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))
150.0ms
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
130.0ms
(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
126.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
Compiler

Compiled 3079 to 2424 computations (21.3% saved)

simplify91.0ms (1.2%)

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049434072
149434072

prune328.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1652167
Fresh044
Picked101
Done011
Total1667173
Error
2.7b
Counts
173 → 7
Compiler

Compiled 6530 to 3920 computations (40% saved)

localize22.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x))))))
0.0b
(sqrt.f64 (*.f64 1/2 (/.f64 (-.f64 1 (/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x))))))))))
0.0b
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
0.0b
(+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x))
3.1b
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
5.3b
(exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))
14.5b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))
17.5b
(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))))

rewrite62.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt_binary64_3169
36×times-frac_binary64_3153
35×*-un-lft-identity_binary64_3147
33×cancel-sign-sub-inv_binary64_3113
29×add-cube-cbrt_binary64_3182
28×exp-sum_binary64_3193 log-prod_binary64_3233
17×sqrt-prod_binary64_3163
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183
difference-of-squares_binary64_3116
pow1_binary64_3208
exp-prod_binary64_3199 add-log-exp_binary64_3186 sqrt-div_binary64_3164
flip-+_binary64_3121 flip3-+_binary64_3150 exp-diff_binary64_3195 associate-/r/_binary64_3093 log-div_binary64_3234
associate-/r*_binary64_3091 log-pow_binary64_3236
cbrt-undiv_binary64_3181 sqrt-pow1_binary64_3165 pow1/2_binary64_3227 div-exp_binary64_3198 div-inv_binary64_3144
flip--_binary64_3122 clear-num_binary64_3146 flip3--_binary64_3151 frac-2neg_binary64_3158 sub-neg_binary64_3140 rem-sqrt-square_binary64_3160 distribute-lft-out--_binary64_3099 prod-exp_binary64_3196 rem-exp-log_binary64_3187 cbrt-unprod_binary64_3180 diff-log_binary64_3239 associate-/l*_binary64_3092
Counts
4 → 113
Calls

8 calls:

23.0ms
(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))))
9.0ms
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
8.0ms
(exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))
0.0ms
(+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x))

series741.0ms (9.5%)

Counts
4 → 61
Calls

4 calls:

261.0ms
(-.f64 1 (/.f64 x (exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))))
190.0ms
(exp.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))))
149.0ms
(/.f64 (*.f64 x x) (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
140.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 p 4)) (*.f64 x x)))
Compiler

Compiled 3570 to 2798 computations (21.6% saved)

simplify76.0ms (1%)

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049203944
149203944

prune338.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1740174
Fresh055
Picked011
Done011
Total1747181
Error
2.7b
Counts
181 → 7
Compiler

Compiled 6790 to 4106 computations (39.5% saved)

simplify25.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
04941462
14941462

regimes180.0ms (2.3%)

Compiler

Compiled 1894 to 1444 computations (23.8% saved)

bsearch29.0ms (0.4%)

Steps
ItersRangePoint
7
-5.673860508701174e+37
-2.236344839210726e+35
-5.541137639902676e+37
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes52.0ms (0.7%)

Compiler

Compiled 238 to 240 computations (-0.8% saved)

bsearch31.0ms (0.4%)

Steps
ItersRangePoint
8
-1.543163530645013e+41
-3.944768162762841e+38
-3.4879622713358363e+40
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes50.0ms (0.6%)

Compiler

Compiled 204 to 212 computations (-3.9% saved)

bsearch30.0ms (0.4%)

Steps
ItersRangePoint
7
-5.673860508701174e+37
-2.236344839210726e+35
-2.23931280946362e+36
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes87.0ms (1.1%)

Compiler

Compiled 116 to 136 computations (-17.2% saved)

bsearch55.0ms (0.7%)

Steps
ItersRangePoint
10
6.868537479139037e-25
9.875411463514256e-13
7.734268629689336e-22
8
-4.534306592275295e+23
-5.7568378030823336e+20
-5.81188855795806e+20
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes66.0ms (0.8%)

Compiler

Compiled 52 to 76 computations (-46.2% saved)

bsearch43.0ms (0.6%)

Steps
ItersRangePoint
10
6.868537479139037e-25
9.875411463514256e-13
5.7469143280990995e-18
5
-9.412380578619078e-38
-3.4554593858931595e-38
-4.411606632062893e-38
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0.2%)

Accuracy

Total 11.7b remaining (80.2%)

Threshold costs 0b (0%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch34.0ms (0.4%)

Steps
ItersRangePoint
7
-5.673860508701174e+37
-2.236344839210726e+35
-2.3222646024626815e+36
Compiler

Compiled 142 to 118 computations (16.9% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087209
187209

end0.0ms (0%)

sample2.0s (26.1%)

Algorithm
intervals
Results
315.0ms6071×body128valid
206.0ms776×body2048valid
152.0ms8000×pre128true
100.0ms503×body1024valid
90.0ms285×body4096valid
36.0ms246×body512valid
12.0ms119×body256valid
Compiler

Compiled 1121 to 866 computations (22.7% saved)

Pareto

0.39228218798969905

Profiling

Loading profile data...