Details

Time bar (total: 8.9s)

analyze684.0ms (7.7%)

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)

sample133.0ms (1.5%)

Algorithm
intervals
Results
13.0ms183×body128valid
10.0ms30×body2048valid
6.0ms11×body4096valid
5.0ms21×body1024valid
3.0ms21×body128nan
1.0msbody512valid
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify262.0ms (2.9%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
27.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
27.8b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
27.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
1.1b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
17.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series257.0ms (2.9%)

Counts
4 → 96
Calls

4 calls:

102.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
96.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
13.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite32.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
10×fma-def_binary64
10×add-cube-cbrt_binary64
10×add-log-exp_binary64
Counts
4 → 90
Calls

4 calls:

10.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
9.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
3.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify126.0ms (1.4%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
314×cancel-sign-sub-inv_binary64
215×distribute-rgt-neg-in_binary64
159×associate-*r*_binary64
150×distribute-rgt-neg-out_binary64
Counts
186 → 207
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434178
16953846
225123724
346923704
450313704

prune189.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New19710207
Fresh011
Picked101
Done000
Total19811209
Error
4.5b
Counts
209 → 11
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
43.8b
(/.f64 (neg.f64 b) a)
49.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 (*.f64 b b) 3) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (*.f64 (*.f64 b b) (*.f64 b b)) (+.f64 (*.f64 (*.f64 (*.f64 4 a) c) (*.f64 (*.f64 4 a) c)) (*.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (*.f64 2 a))
28.0b
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
44.0b
(neg.f64 (/.f64 c b))
28.0b
(*.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) a))
27.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.9b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
27.9b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
31.6b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
Compiler

Compiled 5819 to 3407 computations (41.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.2b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
1.1b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
17.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series380.0ms (4.3%)

Counts
2 → 40
Calls

2 calls:

286.0ms
(/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
93.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite33.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
58×times-frac_binary64
48×*-un-lft-identity_binary64
28×add-exp-log_binary64
24×add-sqr-sqrt_binary64
24×add-cube-cbrt_binary64
Counts
2 → 103
Calls

2 calls:

11.0ms
(/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
11.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify127.0ms (1.4%)

Algorithm
egg-herbie
Rules
522×fma-def_binary64
330×fma-neg_binary64
303×div-sub_binary64
273×distribute-rgt-in_binary64
218×distribute-lft-in_binary64
Counts
143 → 184
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02144744
15994117
221293867
345433867
452203867

prune239.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2855290
Fresh5510
Picked011
Done000
Total29011301
Error
4.5b
Counts
301 → 11
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
43.8b
(/.f64 (neg.f64 b) a)
28.0b
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
44.0b
(neg.f64 (/.f64 c b))
27.9b
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
32.4b
(*.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
31.6b
(/.f64 1 (/.f64 (*.f64 2 a) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
43.8b
(/.f64 1 (neg.f64 (/.f64 a b)))
27.9b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
44.0b
(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
Compiler

Compiled 8928 to 5516 computations (38.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.2b
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
1.1b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
17.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series146.0ms (1.6%)

Counts
2 → 40
Calls

2 calls:

88.0ms
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
58.0ms
(/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite106.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
317×add-exp-log_binary64
244×times-frac_binary64
200×*-un-lft-identity_binary64
164×div-exp_binary64
130×add-sqr-sqrt_binary64
Counts
2 → 319
Calls

2 calls:

32.0ms
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
13.0ms
(/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify242.0ms (2.7%)

Algorithm
egg-herbie
Rules
596×fma-def_binary64
414×fma-neg_binary64
399×distribute-rgt-in_binary64
159×cancel-sign-sub-inv_binary64
129×*-commutative_binary64
Counts
359 → 404
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02779955
16748669
224408214
348038214
449388214

prune407.0ms (4.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New5100510
Fresh099
Picked011
Done011
Total51011521
Error
4.5b
Counts
521 → 11
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
43.8b
(/.f64 (neg.f64 b) a)
28.0b
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
44.0b
(neg.f64 (/.f64 c b))
27.9b
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
32.4b
(*.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
31.6b
(/.f64 1 (/.f64 (*.f64 2 a) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
43.8b
(/.f64 1 (neg.f64 (/.f64 a b)))
27.9b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
44.0b
(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
Compiler

Compiled 17880 to 11882 computations (33.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.3b
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
1.1b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
17.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series882.0ms (9.9%)

Counts
2 → 24
Calls

2 calls:

794.0ms
(/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
88.0ms
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))

rewrite76.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
192×times-frac_binary64
167×*-un-lft-identity_binary64
130×sqrt-prod_binary64
63×add-sqr-sqrt_binary64
63×add-cube-cbrt_binary64
Counts
2 → 190
Calls

2 calls:

22.0ms
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
10.0ms
(/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify264.0ms (3%)

Algorithm
egg-herbie
Rules
668×associate-/r/_binary64
409×div-sub_binary64
379×fma-def_binary64
306×fma-neg_binary64
140×cancel-sign-sub-inv_binary64
Counts
214 → 239
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027913665
170111375
2231610414
345889808
455889808

prune402.0ms (4.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New4510451
Fresh088
Picked011
Done022
Total45111462
Error
4.5b
Counts
462 → 11
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
43.8b
(/.f64 (neg.f64 b) a)
28.0b
(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (*.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
44.0b
(neg.f64 (/.f64 c b))
27.9b
(*.f64 (/.f64 1 (*.f64 2 a)) (/.f64 1 (/.f64 1 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
32.4b
(*.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
31.6b
(/.f64 1 (/.f64 (*.f64 2 a) (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
43.8b
(/.f64 1 (neg.f64 (/.f64 a b)))
27.9b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
44.0b
(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
Compiler

Compiled 21226 to 12507 computations (41.1% saved)

regimes2.1s (23.1%)

Accuracy

Total 3.6b remaining (39.4%)

Threshold costs 0b (0%)

Counts
226 → 4
Compiler

Compiled 22853 to 16431 computations (28.1% saved)

bsearch73.0ms (0.8%)

Steps
ItersRangePoint
6
3.6696017627942624e+35
2.340832439645857e+36
2.258064133565435e+36
7
3.3022087754599802e-87
1.3214269837451072e-85
3.3445021699402826e-87
2
-4.403920044906212e+136
-1.2773442230667882e+136
-1.7992336626316105e+136
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
15×*-commutative_binary64
12×+-commutative_binary64
10×sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04095
16491
29091
310591
411291
511491
611391

end1.0ms (0%)

Compiler

Compiled 64 to 43 computations (32.8% saved)

sample1.7s (19.5%)

Algorithm
intervals
Results
380.0ms5238×body128valid
369.0ms1109×body2048valid
216.0ms762×body1024valid
141.0ms349×body4096valid
72.0ms356×body512valid
49.0ms673×body128nan
29.0ms393×body128invalid
24.0ms186×body256valid
Compiler

Compiled 288 to 203 computations (29.5% saved)

Profiling

Loading profile data...