Details

Time bar (total: 7.8s)

analyze586.0ms (7.5%)

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)

sample43.0ms (0.6%)

Algorithm
intervals
Results
10.0ms162×body128valid
9.0ms36×body2048valid
5.0ms25×body1024valid
4.0ms12×body4096valid
2.0ms14×body512valid
1.0ms27×body128nan
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify330.0ms (4.2%)

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
36.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
36.4b
(/.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)

localize13.0ms (0.2%)

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))
0.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite176.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
36.2b
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)

series252.0ms (3.2%)

Error
5.7b
Counts
4 → 76
Calls

4 calls:

73.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
55.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
41.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 3238 to 2328 computations (28.1% saved)

simplify126.0ms (1.6%)

Algorithm
egg-herbie
Rules
775×associate-/l*_binary64
207×cancel-sign-sub-inv_binary64
204×distribute-rgt-in_binary64
187×distribute-rgt-neg-in_binary64
184×distribute-lft-in_binary64
Counts
150 → 98
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02253457
16143210
219483192
349623192
449893192

prune71.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New89998
Fresh000
Picked011
Done000
Total891099
Error
5.7b
Counts
99 → 10
Alt Table
StatusErrorProgram
36.4b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (*.f64 a 2))
51.2b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 a 2))
36.5b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) (/.f64 1/2 a))
36.4b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
44.1b
(/.f64 (neg.f64 b) a)
36.9b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
49.7b
(-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b))
47.6b
(/.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)))
46.0b
(/.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))
38.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 1662 to 958 computations (42.4% saved)

localize11.0ms (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)))
0.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite396.0ms (5.1%)

Algorithm
rewrite-expression-head
Error
5.7b
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:

26.0ms
(/.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)
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 11060 to 6512 computations (41.1% saved)

series253.0ms (3.2%)

Error
5.7b
Counts
4 → 76
Calls

4 calls:

74.0ms
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
57.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
48.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
43.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 3438 to 2528 computations (26.5% saved)

simplify453.0ms (5.8%)

Algorithm
egg-herbie
Rules
318×associate-/r/_binary64
244×*-commutative_binary64
204×cancel-sign-sub-inv_binary64
197×distribute-rgt-in_binary64 associate-*l/_binary64
182×distribute-rgt-neg-in_binary64
Counts
432 → 384
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043817869
1102716811
2335316507
3468916507
4499016507

prune158.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3804384
Fresh358
Picked011
Done101
Total38410394
Error
5.7b
Counts
394 → 10
Alt Table
StatusErrorProgram
51.2b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) 2)))
36.9b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) a))
44.2b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
44.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -2) 2)))
36.4b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
44.1b
(/.f64 (neg.f64 b) a)
36.9b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
49.7b
(-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b))
46.0b
(/.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))
38.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 5212 to 2875 computations (44.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite94.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
5.7b
Rules
18×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64
pow1_binary64 cancel-sign-sub-inv_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 difference-of-squares_binary64
Counts
4 → 64
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
8.0ms
(-.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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 2485 to 1287 computations (48.2% saved)

series199.0ms (2.6%)

Error
5.7b
Counts
4 → 58
Calls

4 calls:

43.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
42.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
42.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
42.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 4347 to 2906 computations (33.1% saved)

simplify131.0ms (1.7%)

Algorithm
egg-herbie
Rules
504×associate-*l*_binary64
488×associate-*r*_binary64
394×times-frac_binary64
311×div-sub_binary64
227×distribute-neg-frac_binary64
Counts
122 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01122346
12842272
27912266
338492242
447752242
552362242

prune63.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New62062
Fresh088
Picked011
Done011
Total621072
Error
5.7b
Counts
72 → 10
Alt Table
StatusErrorProgram
51.2b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) 2)))
36.9b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) a))
44.2b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
44.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -2) 2)))
36.4b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
44.1b
(/.f64 (neg.f64 b) a)
36.9b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
49.7b
(-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b))
46.0b
(/.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))
38.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 2066 to 1226 computations (40.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
0.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
24.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite100.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
5.7b
Rules
18×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64
pow1_binary64 cancel-sign-sub-inv_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 difference-of-squares_binary64
Counts
4 → 64
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
8.0ms
(-.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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 2601 to 1403 computations (46.1% saved)

series205.0ms (2.6%)

Error
5.7b
Counts
4 → 58
Calls

4 calls:

46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
45.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
42.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
42.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)
Compiler

Compiled 4579 to 3139 computations (31.4% saved)

simplify127.0ms (1.6%)

Algorithm
egg-herbie
Rules
504×associate-*l*_binary64
488×associate-*r*_binary64
394×times-frac_binary64
311×div-sub_binary64
227×distribute-neg-frac_binary64
Counts
122 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01122346
12842272
27912266
338492242
447752242
552362242

prune62.0ms (0.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New62062
Fresh077
Picked011
Done022
Total621072
Error
5.7b
Counts
72 → 10
Alt Table
StatusErrorProgram
51.2b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) 2)))
36.9b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)) a))
44.2b
(/.f64 1 (/.f64 a (/.f64 (*.f64 b -2) 2)))
44.7b
(/.f64 1 (/.f64 a (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -2) 2)))
36.4b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
44.1b
(/.f64 (neg.f64 b) a)
36.9b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
49.7b
(-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b))
46.0b
(/.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))
38.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 1998 to 1211 computations (39.4% saved)

regimes2.4s (30.8%)

Accuracy

Total 4.3b remaining (42.9%)

Threshold costs 0b (0%)

Compiler

Compiled 17012 to 11610 computations (31.8% saved)

bsearch65.0ms (0.8%)

Steps
ItersRangePoint
9
1.4249619272964188e-81
7.241482398477653e-75
1.3130193607872862e-79
9
-2.1039560221547947e+105
-6.739291890968829e+97
-1.1851329742667057e+105
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02754
14254
25954
37654
48854
59354
69454
79354

end1.0ms (0%)

Compiler

Compiled 39 to 26 computations (33.3% saved)

sample1.4s (18.4%)

Algorithm
intervals
Results
296.0ms1183×body2048valid
263.0ms5176×body128valid
138.0ms745×body1024valid
113.0ms386×body4096valid
53.0ms353×body512valid
33.0ms644×body128nan
17.0ms352×body128invalid
14.0ms157×body256valid
Compiler

Compiled 274 to 184 computations (32.8% saved)

Profiling

Loading profile data...