Details

Time bar (total: 9.8s)

analyze523.0ms (5.4%)

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
6.2%93.6%0.2%8
25%74.9%0.2%9
28.1%71.7%0.2%10
29.6%70.2%0.2%11
53%46.8%0.2%12
71.3%28.5%0.2%13
71.7%28.1%0.2%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample24.0ms (0.2%)

Algorithm
intervals
Results
11.0ms256×body128valid
1.0ms14×body128invalid
Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify221.0ms (2.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (125.0ms)

IterNodesCost
0523022

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
27.3b
Counts
2 → 1
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

26.8b
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))
0.2b
(-.f64 (*.f64 b c) (*.f64 a d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.2b
(-.f64 (*.f64 b c) (*.f64 a d))
26.8b
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64_3147 add-sqr-sqrt_binary64_3169 add-cube-cbrt_binary64_3182
times-frac_binary64_3153
add-log-exp_binary64_3186
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183
associate-/r*_binary64_3091 pow1_binary64_3208 associate-/l*_binary64_3092
flip--_binary64_3122 flip-+_binary64_3121 flip3--_binary64_3151 flip3-+_binary64_3150 associate-/l/_binary64_3094 associate-/r/_binary64_3093
clear-num_binary64_3146 cancel-sign-sub-inv_binary64_3113 frac-2neg_binary64_3158 sub-neg_binary64_3140 +-commutative_binary64_3077 div-sub_binary64_3152 cbrt-undiv_binary64_3181 div-exp_binary64_3198 diff-log_binary64_3239 div-inv_binary64_3144 sum-log_binary64_3238
Counts
3 → 55
Calls

6 calls:

10.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(+.f64 (*.f64 c c) (*.f64 d d))
4.0ms
(-.f64 (*.f64 b c) (*.f64 a d))
0.0ms
(+.f64 (*.f64 c c) (*.f64 d d))
0.0ms
(-.f64 (*.f64 b c) (*.f64 a d))

series564.0ms (5.8%)

Counts
3 → 63
Calls

3 calls:

335.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))
143.0ms
(-.f64 (*.f64 b c) (*.f64 a d))
86.0ms
(+.f64 (*.f64 c c) (*.f64 d d))
Compiler

Compiled 1407 to 1170 computations (16.8% saved)

simplify79.0ms (0.8%)

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
061562125

prune150.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh000
Picked101
Done000
Total10910119
Error
4.2b
Counts
119 → 10
Compiler

Compiled 2381 to 338 computations (85.8% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(-.f64 (*.f64 b c) (*.f64 a d))
0.1b
(/.f64 (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.2b
(-.f64 (*.f64 b c) (*.f64 a d))
17.8b
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64_3169
21×*-un-lft-identity_binary64_3147 add-cube-cbrt_binary64_3182
18×times-frac_binary64_3153 sqrt-prod_binary64_3163
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 associate-/r*_binary64_3091 pow1_binary64_3208 add-log-exp_binary64_3186 sqrt-div_binary64_3164
flip-+_binary64_3121 flip3-+_binary64_3150 associate-/l*_binary64_3092
flip--_binary64_3122 flip3--_binary64_3151 associate-/l/_binary64_3094 rem-sqrt-square_binary64_3160 sqrt-pow1_binary64_3165 pow1/2_binary64_3227 associate-/r/_binary64_3093
clear-num_binary64_3146 cancel-sign-sub-inv_binary64_3113 frac-2neg_binary64_3158 sub-neg_binary64_3140 div-sub_binary64_3152 cbrt-undiv_binary64_3181 div-exp_binary64_3198 diff-log_binary64_3239 div-inv_binary64_3144
Counts
4 → 86
Calls

8 calls:

11.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(-.f64 (*.f64 b c) (*.f64 a d))
0.0ms
(+.f64 (*.f64 c c) (*.f64 d d))

series797.0ms (8.2%)

Counts
4 → 94
Calls

4 calls:

415.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
153.0ms
(-.f64 (*.f64 b c) (*.f64 a d))
115.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
114.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
Compiler

Compiled 3466 to 2444 computations (29.5% saved)

simplify98.0ms (1%)

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049633760
149633760

prune164.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1764180
Fresh189
Picked101
Done000
Total17812190
Error
4.2b
Counts
190 → 12
Compiler

Compiled 5583 to 842 computations (84.9% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))) (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))))
0.2b
(-.f64 (*.f64 b c) (*.f64 a d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))) (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))))
17.8b
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))

rewrite69.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt_binary64_3169
76×times-frac_binary64_3153
53×*-un-lft-identity_binary64_3147
47×add-cube-cbrt_binary64_3182 sqrt-prod_binary64_3163
28×add-exp-log_binary64_3185
24×associate-*r*_binary64_3087 associate-*l*_binary64_3088
18×add-cbrt-cube_binary64_3183
15×unswap-sqr_binary64_3115
10×sqrt-div_binary64_3164
div-exp_binary64_3198
pow1_binary64_3208 prod-exp_binary64_3196
associate-/r*_binary64_3091 associate-/r/_binary64_3093
flip-+_binary64_3121 flip3-+_binary64_3150 cbrt-undiv_binary64_3181
cbrt-unprod_binary64_3180 add-log-exp_binary64_3186
associate-/l*_binary64_3092 div-inv_binary64_3144
associate-/l/_binary64_3094 rem-sqrt-square_binary64_3160 sqrt-pow1_binary64_3165 pow1/2_binary64_3227 1-exp_binary64_3191 rec-exp_binary64_3197
*-commutative_binary64_3078 frac-times_binary64_3157 flip--_binary64_3122 clear-num_binary64_3146 pow-prod-down_binary64_3218 associate-*l/_binary64_3090 flip3--_binary64_3151 frac-2neg_binary64_3158 div-sub_binary64_3152 associate-*r/_binary64_3089
Counts
4 → 161
Calls

8 calls:

30.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))) (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))))
10.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
0.0ms
(+.f64 (*.f64 c c) (*.f64 d d))

series984.0ms (10.1%)

Counts
4 → 97
Calls

4 calls:

424.0ms
(/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
327.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))) (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))))
119.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
113.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
Compiler

Compiled 3435 to 2734 computations (20.4% saved)

simplify126.0ms (1.3%)

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049667570
149667570

prune239.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2562258
Fresh3811
Picked011
Done000
Total25911270
Error
4.0b
Counts
270 → 11
Compiler

Compiled 8526 to 1422 computations (83.3% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))) (/.f64 (-.f64 (*.f64 c b) (*.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))))) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
9.6b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))) (/.f64 (-.f64 (*.f64 c b) (*.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
27.8b
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))

rewrite80.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
137×add-sqr-sqrt_binary64_3169
108×sqrt-prod_binary64_3163
99×times-frac_binary64_3153
57×*-un-lft-identity_binary64_3147
45×add-cube-cbrt_binary64_3182
33×associate-*r*_binary64_3087 associate-*l*_binary64_3088
28×unswap-sqr_binary64_3115
26×add-exp-log_binary64_3185
16×add-cbrt-cube_binary64_3183
14×sqrt-div_binary64_3164
pow1_binary64_3208
prod-exp_binary64_3196 div-exp_binary64_3198
flip-+_binary64_3121 flip3-+_binary64_3150
cbrt-undiv_binary64_3181 cbrt-unprod_binary64_3180 add-log-exp_binary64_3186 associate-/r/_binary64_3093
rem-sqrt-square_binary64_3160 sqrt-pow1_binary64_3165 pow1/2_binary64_3227
1-exp_binary64_3191 rec-exp_binary64_3197 div-inv_binary64_3144
*-commutative_binary64_3078 frac-times_binary64_3157 pow-prod-down_binary64_3218 associate-*l/_binary64_3090 associate-*r/_binary64_3089
Counts
4 → 163
Calls

8 calls:

40.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))) (/.f64 (-.f64 (*.f64 c b) (*.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
0.0ms
(+.f64 (*.f64 c c) (*.f64 d d))

series802.0ms (8.2%)

Counts
4 → 89
Calls

4 calls:

428.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))) (/.f64 (-.f64 (*.f64 c b) (*.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d))))))
127.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
124.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
123.0ms
(sqrt.f64 (+.f64 (*.f64 c c) (*.f64 d d)))
Compiler

Compiled 4333 to 2925 computations (32.5% saved)

simplify115.0ms (1.2%)

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049698321
149698321

prune253.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2520252
Fresh099
Picked011
Done011
Total25211263
Error
4.0b
Counts
263 → 11
Compiler

Compiled 11138 to 1507 computations (86.5% saved)

simplify23.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
03801514
13801514

regimes786.0ms (8%)

Compiler

Compiled 4024 to 2320 computations (42.3% saved)

bsearch83.0ms (0.8%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
2.0139063475555305e+69
9
1.5985712979139024e-152
5.795803614072852e-145
1.8192329406445362e-149
9
-7.750398627192034e-42
-7.035472584919937e-50
-8.232708701844971e-48
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-3.2563987087522574e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes487.0ms (5%)

Compiler

Compiled 1644 to 1316 computations (20% saved)

bsearch77.0ms (0.8%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
1.2069815748150215e+69
9
1.5985712979139024e-152
5.795803614072852e-145
1.3404554011445771e-145
9
-7.750398627192034e-42
-7.035472584919937e-50
-1.644763038826746e-49
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-2.3901732992931246e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes272.0ms (2.8%)

Compiler

Compiled 404 to 428 computations (-5.9% saved)

bsearch71.0ms (0.7%)

Steps
ItersRangePoint
10
6.403146828535289e-69
3.9650914253789193e-53
1.2863457966181983e-53
10
-0.03564989410319676
-5.701297150438165e-15
-1.418363775640226e-12
2
-1.757910962160964e+59
-1.5703142594340002e+59
-1.6406630229566118e+59
10
-2.1449544966000207e+94
-1.4008730392468882e+84
-2.6251436529546742e+85
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes244.0ms (2.5%)

Compiler

Compiled 312 to 352 computations (-12.8% saved)

bsearch68.0ms (0.7%)

Steps
ItersRangePoint
10
6.403146828535289e-69
3.9650914253789193e-53
1.928153543830285e-57
10
-0.03564989410319676
-5.701297150438165e-15
-2.8002525199011073e-10
2
-1.757910962160964e+59
-1.5703142594340002e+59
-1.7344613743200935e+59
8
-3.702281864159641e+74
-6.13376548996517e+71
-7.490156733069174e+71
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes175.0ms (1.8%)

Compiler

Compiled 180 to 244 computations (-35.6% saved)

bsearch71.0ms (0.7%)

Steps
ItersRangePoint
9
2.9440458580396446e+54
2.424121438622175e+63
5.475526172947629e+56
10
6.981770734925066e+31
3.110364680802558e+44
2.707692421836616e+44
7
1.2799929126807054e-59
9.280121754331065e-58
7.897694579240514e-58
8
-1.830820577979186e-12
-5.592649249220658e-17
-5.012823408298066e-13
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes144.0ms (1.5%)

Compiler

Compiled 92 to 172 computations (-87% saved)

bsearch76.0ms (0.8%)

Steps
ItersRangePoint
9
2.9440458580396446e+54
2.424121438622175e+63
5.565175323815072e+54
10
6.981770734925066e+31
3.110364680802558e+44
1.7115989933157516e+32
10
1.5006327099674739e-05
186394172660.0271
5512952.078642197
8
-1.830820577979186e-12
-5.592649249220658e-17
-2.648659214426478e-13
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes104.0ms (1.1%)

Compiler

Compiled 48 to 136 computations (-183.3% saved)

bsearch29.0ms (0.3%)

Steps
ItersRangePoint
7
4.980887860223029e-07
0.00010323440451509003
2.6785472288895752e-06
8
-3.702281864159641e+74
-6.13376548996517e+71
-6.213553210147759e+71
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes64.0ms (0.7%)

Compiler

Compiled 32 to 112 computations (-250% saved)

bsearch28.0ms (0.3%)

Steps
ItersRangePoint
8
2.443870323434491e+43
1.5554586086373416e+46
1.5347938031871036e+46
7
-1.466580252871722e+116
-5.105510058682821e+114
-2.520179551920492e+115
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes33.0ms (0.3%)

Accuracy

Total 10.1b remaining (68.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch15.0ms (0.2%)

Compiler

Compiled 456 to 202 computations (55.7% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0215586
1215586

end0.0ms (0%)

sample1.5s (15.4%)

Algorithm
intervals
Results
333.0ms8000×body128valid
22.0ms477×body128invalid
Compiler

Compiled 1454 to 817 computations (43.8% saved)

Pareto

0.9236603496914346

Profiling

Loading profile data...