Details

Time bar (total: 10.6s)

analyze454.0ms (4.3%)

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
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.4%)

Algorithm
intervals
Results
11.0ms45×body2048valid
8.0ms160×body128valid
4.0ms14×body4096valid
3.0ms19×body1024valid
3.0msbody128invalid
2.0ms13×body512valid
1.0ms21×body128nan
0.0msbody256valid
Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify425.0ms (4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (330.0ms)

IterNodesCost
0183424
1183424

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
36.7b
Counts
2 → 1
Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
0.0b
(*.f64 4 (*.f64 a c))
0.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
0.6b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite39.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64_2806
20×add-sqr-sqrt_binary64_2828
16×associate-*r*_binary64_2746
14×add-cube-cbrt_binary64_2841
13×times-frac_binary64_2812
add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842
add-log-exp_binary64_2845
pow1_binary64_2867
distribute-lft-out_binary64_2757
associate-*l*_binary64_2747 sqrt-prod_binary64_2822
sqrt-div_binary64_2823 flip3--_binary64_2810 prod-exp_binary64_2855 cbrt-unprod_binary64_2839 flip--_binary64_2781 unswap-sqr_binary64_2774
pow1/2_binary64_2886 cancel-sign-sub-inv_binary64_2772 div-inv_binary64_2803 div-exp_binary64_2857 *-commutative_binary64_2737 cbrt-undiv_binary64_2840 sqrt-pow1_binary64_2824 diff-log_binary64_2898 sub-neg_binary64_2799 rem-sqrt-square_binary64_2819 flip-+_binary64_2780 sum-log_binary64_2897 flip3-+_binary64_2809 associate-*r/_binary64_2748 pow-prod-down_binary64_2877 +-commutative_binary64_2736
Counts
4 → 74
Calls

8 calls:

13.0ms
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
8.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 4 (*.f64 a c))

series691.0ms (6.5%)

Counts
4 → 76
Calls

4 calls:

226.0ms
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
161.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
152.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
151.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 2172 to 1828 computations (15.8% saved)

simplify92.0ms (0.9%)

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049362958
149362958

prune218.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1437150
Fresh000
Picked101
Done000
Total1447151
Error
6.6b
Counts
151 → 7
Compiler

Compiled 3089 to 1620 computations (47.6% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a))
1.2b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.3b
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
10.2b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite57.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64_2812
59×add-sqr-sqrt_binary64_2828
44×*-un-lft-identity_binary64_2806
30×add-cube-cbrt_binary64_2841
27×add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842
14×difference-of-squares_binary64_2775
13×sqrt-prod_binary64_2822 associate-/l*_binary64_2751
10×div-exp_binary64_2857 cbrt-undiv_binary64_2840 associate-/r/_binary64_2752
associate-/r*_binary64_2750
flip3--_binary64_2810 distribute-lft-out--_binary64_2758 flip--_binary64_2781
cancel-sign-sub-inv_binary64_2772 div-inv_binary64_2803 prod-exp_binary64_2855 cbrt-unprod_binary64_2839 add-log-exp_binary64_2845
pow1_binary64_2867
sqrt-div_binary64_2823 clear-num_binary64_2805 frac-2neg_binary64_2817
associate-/l/_binary64_2753 pow1/2_binary64_2886 sqrt-pow1_binary64_2824 diff-log_binary64_2898 sub-neg_binary64_2799 rem-sqrt-square_binary64_2819
Counts
4 → 136
Calls

8 calls:

14.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
12.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
10.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a))

series1.0s (9.5%)

Counts
4 → 73
Calls

4 calls:

350.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
331.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
164.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
157.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 3049 to 2389 computations (21.6% saved)

simplify104.0ms (1%)

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049426184
149426184

prune294.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2063209
Fresh246
Picked101
Done000
Total2097216
Error
6.6b
Counts
216 → 7
Compiler

Compiled 6002 to 3117 computations (48.1% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
0.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))
0.1b
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.2b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite37.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64_2828
28×*-un-lft-identity_binary64_2806
18×times-frac_binary64_2812 add-cube-cbrt_binary64_2841
11×sqrt-prod_binary64_2822
10×difference-of-squares_binary64_2775
add-log-exp_binary64_2845
cancel-sign-sub-inv_binary64_2772
add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842 associate-/r*_binary64_2750
distribute-lft-out--_binary64_2758 pow1_binary64_2867
flip3--_binary64_2810 flip--_binary64_2781
associate-/l*_binary64_2751
sqrt-div_binary64_2823 diff-log_binary64_2898 sub-neg_binary64_2799 associate-/r/_binary64_2752
pow1/2_binary64_2886 div-inv_binary64_2803 div-exp_binary64_2857 cbrt-undiv_binary64_2840 sqrt-pow1_binary64_2824 rem-sqrt-square_binary64_2819 clear-num_binary64_2805 frac-2neg_binary64_2817
Counts
4 → 88
Calls

8 calls:

10.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
9.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))

series752.0ms (7.1%)

Counts
4 → 73
Calls

4 calls:

287.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
163.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
154.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
147.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 2690 to 2305 computations (14.3% saved)

simplify79.0ms (0.7%)

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049833577
149833577

prune201.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1610161
Fresh066
Picked011
Done000
Total1617168
Error
6.6b
Counts
168 → 7
Compiler

Compiled 4145 to 2465 computations (40.5% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))) a))
9.8b
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
10.7b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_2828 add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842
*-un-lft-identity_binary64_2806 add-cube-cbrt_binary64_2841
add-log-exp_binary64_2845 sqrt-prod_binary64_2822 pow1_binary64_2867
sqrt-div_binary64_2823 times-frac_binary64_2812 flip3--_binary64_2810 associate-/r*_binary64_2750 flip--_binary64_2781
div-exp_binary64_2857 cbrt-undiv_binary64_2840 prod-exp_binary64_2855 cbrt-unprod_binary64_2839 difference-of-squares_binary64_2775
pow1/2_binary64_2886 sqrt-pow1_binary64_2824 rem-sqrt-square_binary64_2819 associate-/r/_binary64_2752
cancel-sign-sub-inv_binary64_2772 div-inv_binary64_2803 diff-log_binary64_2898 sub-neg_binary64_2799 clear-num_binary64_2805 associate-/l*_binary64_2751 frac-2neg_binary64_2817
Counts
4 → 70
Calls

8 calls:

9.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
3.0ms
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
0.0ms
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))) a))

series878.0ms (8.3%)

Counts
4 → 75
Calls

4 calls:

370.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
177.0ms
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
166.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
164.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 3906 to 2901 computations (25.7% saved)

simplify63.0ms (0.6%)

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
052363195

prune201.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh055
Picked011
Done011
Total1457152
Error
6.6b
Counts
152 → 7
Compiler

Compiled 4833 to 2486 computations (48.6% saved)

simplify28.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
05271626
15271626

regimes859.0ms (8.1%)

Compiler

Compiled 3207 to 2457 computations (23.4% saved)

bsearch95.0ms (0.9%)

Steps
ItersRangePoint
9
1.1935307154283341e+95
4.0136306422491975e+100
5.513576328640909e+99
5
2.3280598367501807e-277
6.026491473597822e-277
3.201370751245736e-277
9
-1.0451269989421558e+143
-1.1049780562537373e+138
-1.303984552860991e+140
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes284.0ms (2.7%)

Compiler

Compiled 609 to 573 computations (5.9% saved)

bsearch49.0ms (0.5%)

Steps
ItersRangePoint
9
1.1935307154283341e+95
4.0136306422491975e+100
3.0794489170197573e+97
6
-5.781806328546769e-124
-8.565900891222301e-125
-3.935594578192137e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes227.0ms (2.1%)

Compiler

Compiled 354 to 360 computations (-1.7% saved)

bsearch49.0ms (0.5%)

Steps
ItersRangePoint
9
1.1935307154283341e+95
4.0136306422491975e+100
1.074781288605891e+99
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.7015362524443945e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes184.0ms (1.7%)

Compiler

Compiled 306 to 321 computations (-4.9% saved)

bsearch49.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
5.463562378517519e-60
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.540996100239644e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes179.0ms (1.7%)

Compiler

Compiled 270 to 288 computations (-6.7% saved)

bsearch50.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
1.192658630200912e-59
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.7015362524443945e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes162.0ms (1.5%)

Compiler

Compiled 234 to 252 computations (-7.7% saved)

bsearch50.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
7.407419570212213e-60
6
-5.781806328546769e-124
-8.565900891222301e-125
-4.41721503480639e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes113.0ms (1.1%)

Compiler

Compiled 204 to 222 computations (-8.8% saved)

bsearch7.0ms (0.1%)

Steps
ItersRangePoint
2
-3.4555292518757554e-207
-3.087791938118972e-207
-3.1124603004849597e-207
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes61.0ms (0.6%)

Compiler

Compiled 27 to 69 computations (-155.6% saved)

bsearch33.0ms (0.3%)

Steps
ItersRangePoint
10
-2.5274467147638208e-288
-1.661289725881152e-300
-1.69076544914991e-300
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes26.0ms (0.2%)

Accuracy

Total 1.1b remaining (16.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch11.0ms (0.1%)

Compiler

Compiled 241 to 173 computations (28.2% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0165357
1165357

end0.0ms (0%)

sample2.3s (22.1%)

Algorithm
intervals
Results
280.0ms1159×body2048valid
261.0ms5195×body128valid
130.0ms680×body1024valid
125.0ms419×body4096valid
50.0ms362×body512valid
32.0ms680×body128nan
22.0ms396×body128invalid
17.0ms185×body256valid
Compiler

Compiled 1368 to 1031 computations (24.6% saved)

Pareto

0.28280816879499904

Profiling

Loading profile data...