Details

Time bar (total: 9.6s)

analyze589.0ms (6.2%)

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 21 to 15 computations (28.6% saved)

sample42.0ms (0.4%)

Algorithm
intervals
Results
9.0ms39×body2048valid
8.0ms160×body128valid
6.0ms19×body4096valid
4.0ms19×body1024valid
2.0ms16×body512valid
1.0ms24×body128nan
0.0msbody128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify343.0ms (3.6%)

Algorithm
egg-herbie
Rules
1228×associate-/l*_binary64
1150×div-sub_binary64
630×distribute-rgt-in_binary64
619×times-frac_binary64
588×associate-/r*_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13324
26224
312124
417224
528224
646024
774824
8108424
9112824
10179924
11259424
12200124
13208924
14215324
15217924
16243124
17290924
18291324
19299124
20305324
21306524
22303524
23321124
24321124
25204324
26219524
27209724
28210724
29210724
30210724
31210724
32183424

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
35.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
35.6b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
Compiler

Compiled 57 to 39 computations (31.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
0.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
25.9b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite163.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
35.4b
Rules
21×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 add-cube-cbrt_binary64
sqrt-prod_binary64 difference-of-squares_binary64 times-frac_binary64 associate-/l*_binary64
Counts
4 → 74
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
7.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 1903 to 985 computations (48.2% saved)

series261.0ms (2.7%)

Error
5.9b
Counts
4 → 85
Calls

4 calls:

76.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
58.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
49.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
40.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 3417 to 2456 computations (28.1% saved)

simplify110.0ms (1.1%)

Algorithm
egg-herbie
Rules
728×associate-/l*_binary64
230×distribute-rgt-in_binary64
197×distribute-lft-in_binary64
192×cancel-sign-sub-inv_binary64
190×distribute-rgt-neg-in_binary64
Counts
159 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02303959
16373664
220553640
351093640

prune74.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New998107
Fresh000
Picked101
Done000
Total1008108
Error
5.9b
Counts
108 → 8
Alt Table
StatusErrorProgram
38.6b
(neg.f64 (/.f64 c b))
45.3b
(*.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a) (/.f64 b a)))
52.3b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 a 2))
47.0b
(/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 b b)) (*.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 a 2)))
52.1b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2)) 3))
35.6b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
44.3b
(/.f64 (/.f64 (-.f64 (*.f64 b b) (+.f64 (*.f64 4 (*.f64 a c)) (*.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
46.6b
(/.f64 (neg.f64 b) a)
Compiler

Compiled 1635 to 915 computations (44% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
0.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
25.9b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite416.0ms (4.4%)

Algorithm
rewrite-expression-head
Error
5.8b
Rules
693×times-frac_binary64
439×add-sqr-sqrt_binary64
364×*-un-lft-identity_binary64
290×add-cube-cbrt_binary64
74×difference-of-squares_binary64
Counts
4 → 356
Calls

4 calls:

24.0ms
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 11060 to 6512 computations (41.1% saved)

series256.0ms (2.7%)

Error
5.9b
Counts
4 → 85
Calls

4 calls:

74.0ms
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
62.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
49.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
39.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 3627 to 2666 computations (26.5% saved)

simplify417.0ms (4.4%)

Algorithm
egg-herbie
Rules
480×associate-/r/_binary64
338×*-commutative_binary64
332×associate-*l/_binary64
279×associate-/l/_binary64
273×associate-*r/_binary64
Counts
441 → 379
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054619069
1135218158
2478718157
3498218157

prune210.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3745379
Fresh347
Picked101
Done000
Total3789387
Error
5.8b
Counts
387 → 9
Alt Table
StatusErrorProgram
46.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
38.6b
(neg.f64 (/.f64 c b))
45.3b
(*.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a) (/.f64 b a)))
52.3b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 a 2))
35.6b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
36.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 a) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2))))
36.0b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 1 (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2))))
46.6b
(/.f64 (neg.f64 b) a)
44.3b
(/.f64 1 (/.f64 a (/.f64 (/.f64 (-.f64 (*.f64 b b) (+.f64 (*.f64 4 (*.f64 a c)) (*.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) 2)))
Compiler

Compiled 6816 to 3867 computations (43.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
0.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
25.9b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite261.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
5.8b
Rules
132×times-frac_binary64
83×associate-*r*_binary64
80×add-sqr-sqrt_binary64
77×*-un-lft-identity_binary64
75×add-cube-cbrt_binary64
Counts
4 → 162
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 6128 to 4216 computations (31.2% saved)

series288.0ms (3%)

Error
5.8b
Counts
4 → 85
Calls

4 calls:

75.0ms
(*.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
68.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
60.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
48.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 4362 to 3401 computations (22% saved)

simplify242.0ms (2.5%)

Algorithm
egg-herbie
Rules
678×associate-*l*_binary64
563×associate-*r*_binary64
312×associate-/l*_binary64
272×associate-*r/_binary64
191×associate-/r/_binary64
Counts
247 → 182
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04038698
111976951
247486951
349516951
449616951

prune143.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1793182
Fresh178
Picked101
Done000
Total18110191
Error
5.8b
Counts
191 → 10
Alt Table
StatusErrorProgram
46.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
38.6b
(neg.f64 (/.f64 c b))
45.3b
(*.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a) (/.f64 b a)))
52.3b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 a 2))
50.6b
(*.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (sqrt.f64 a)) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 a) 1/2)))
44.3b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (/.f64 a 1/2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))
36.0b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 1 (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2))))
46.6b
(/.f64 (neg.f64 b) a)
44.3b
(/.f64 1 (/.f64 a (/.f64 (/.f64 (-.f64 (*.f64 b b) (+.f64 (*.f64 4 (*.f64 a c)) (*.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) 2)))
46.6b
(*.f64 (*.f64 (*.f64 b -2) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
Compiler

Compiled 3636 to 2354 computations (35.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
25.9b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
25.9b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite81.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
5.8b
Rules
add-log-exp_binary64 add-sqr-sqrt_binary64
pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
4 → 54
Calls

4 calls:

5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 2279 to 1229 computations (46.1% saved)

series238.0ms (2.5%)

Error
5.8b
Counts
4 → 80
Calls

4 calls:

56.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
56.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
48.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
47.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 5285 to 3618 computations (31.5% saved)

simplify105.0ms (1.1%)

Algorithm
egg-herbie
Rules
604×associate-*l*_binary64
580×associate-*r*_binary64
566×times-frac_binary64
265×associate-/l*_binary64
247×associate-/r*_binary64
Counts
134 → 86
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0922412
12452286
28062286
348362286
449752286

prune53.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New86086
Fresh099
Picked011
Done000
Total861096
Error
5.8b
Counts
96 → 10
Alt Table
StatusErrorProgram
46.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
38.6b
(neg.f64 (/.f64 c b))
45.3b
(*.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a) (/.f64 b a)))
52.3b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 a 2))
50.6b
(*.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (sqrt.f64 a)) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 a) 1/2)))
44.3b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (/.f64 a 1/2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))
36.0b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 1 (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2))))
46.6b
(/.f64 (neg.f64 b) a)
44.3b
(/.f64 1 (/.f64 a (/.f64 (/.f64 (-.f64 (*.f64 b b) (+.f64 (*.f64 4 (*.f64 a c)) (*.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) 2)))
46.6b
(*.f64 (*.f64 (*.f64 b -2) (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (cbrt.f64 1) (/.f64 a 1/2)))
Compiler

Compiled 1811 to 1048 computations (42.1% saved)

regimes3.7s (38.7%)

Accuracy

Total 5.8b remaining (50.7%)

Threshold costs 0b (0%)

Compiler

Compiled 25168 to 17646 computations (29.9% saved)

bsearch44.0ms (0.5%)

Steps
ItersRangePoint
8
5.510773643987163e+27
6.278378928778985e+30
5.608699537249006e+27
2
-1.3801778280206036e+151
-4.953506238584051e+150
-1.0925810582265431e+151
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×sub-neg_binary64 *-commutative_binary64 +-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
distribute-neg-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02758
14258
26158
37958
49158
59658
69758
79658

end1.0ms (0%)

Compiler

Compiled 42 to 26 computations (38.1% saved)

sample1.5s (15.2%)

Algorithm
intervals
Results
281.0ms1138×body2048valid
260.0ms5149×body128valid
139.0ms429×body4096valid
136.0ms731×body1024valid
53.0ms387×body512valid
29.0ms618×body128nan
18.0ms166×body256valid
18.0ms361×body128invalid
Compiler

Compiled 271 to 181 computations (33.2% saved)

Profiling

Loading profile data...