Details

Time bar (total: 6.9s)

analyze723.0ms (10.4%)

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)

sample40.0ms (0.6%)

Algorithm
intervals
Results
8.0ms34×body2048valid
8.0ms168×body128valid
4.0ms21×body1024valid
3.0ms10×body4096valid
3.0ms18×body512valid
1.0ms19×body128nan
1.0ms13×body128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify324.0ms (4.7%)

Algorithm
egg-herbie
Rules
1319×div-sub_binary64
932×unsub-neg_binary64
843×associate-/l*_binary64
678×distribute-rgt-in_binary64
643×distribute-lft-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01526
13726
29326
321324
432024
552224
691324
799524
8115424
9180624
10266324
11235624
12230324
13237224
14239824
15258524
16388124
17356324
18339724
19350524
20350924
21362324
22369124
23369124
24216324
25236324
26208124
27208324
28208324
29208324
30183424

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
32.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
32.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
0.8b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
20.3b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite153.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
32.0b
Rules
24×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
add-log-exp_binary64
Counts
4 → 72
Calls

4 calls:

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

Compiled 1906 to 971 computations (49.1% saved)

series236.0ms (3.4%)

Error
6.3b
Counts
4 → 84
Calls

4 calls:

58.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
50.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
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 3243 to 2324 computations (28.3% saved)

simplify130.0ms (1.9%)

Algorithm
egg-herbie
Rules
957×times-frac_binary64
504×associate-/l*_binary64
257×cancel-sign-sub-inv_binary64
166×distribute-rgt-neg-in_binary64
154×distribute-lft-neg-in_binary64
Counts
156 → 92
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01903668
14863449
214803431
349093431
449483431

prune68.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New83992
Fresh000
Picked011
Done000
Total831093
Error
9.4b
Counts
93 → 10
Alt Table
StatusErrorProgram
32.6b
(*.f64 -1/2 (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)))
32.1b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a))
46.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
46.5b
(*.f64 -1/2 (*.f64 2 (+.f64 (/.f64 c b) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))))
49.3b
(*.f64 -1/2 (/.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) a))
58.0b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
32.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
32.8b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (cbrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)))
43.8b
(*.f64 -1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
46.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
Compiler

Compiled 1565 to 906 computations (42.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.9b
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
11.2b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
20.3b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite189.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
66×times-frac_binary64
59×add-sqr-sqrt_binary64
44×*-un-lft-identity_binary64
30×add-cube-cbrt_binary64
27×add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 136
Calls

4 calls:

13.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
11.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
6.0ms
(-.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))))
Compiler

Compiled 4706 to 2367 computations (49.7% saved)

series329.0ms (4.8%)

Error
8.7b
Counts
4 → 86
Calls

4 calls:

93.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
82.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
63.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
51.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 4659 to 3229 computations (30.7% saved)

simplify266.0ms (3.8%)

Algorithm
egg-herbie
Rules
359×cancel-sign-sub-inv_binary64
263×associate-/l*_binary64
260×times-frac_binary64
176×sub-neg_binary64
165×associate-/r*_binary64
Counts
222 → 154
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03307748
19037060
233776917
348486917
449786917
549666917

prune113.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1486154
Fresh448
Picked101
Done011
Total15311164
Error
8.3b
Counts
164 → 11
Alt Table
StatusErrorProgram
46.7b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (*.f64 b 2)) a))
46.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
46.5b
(*.f64 -1/2 (*.f64 2 (+.f64 (/.f64 c b) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))))
32.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
43.8b
(*.f64 -1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
29.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))
45.5b
(*.f64 -1/2 (exp.f64 (log.f64 (/.f64 4 (*.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) c))))))
32.1b
(*.f64 -1/2 (*.f64 (*.f64 (/.f64 4 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (*.f64 a c)) (/.f64 (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (cbrt.f64 a))))
29.9b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (/.f64 4 (*.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) c)))) (cbrt.f64 (/.f64 4 (*.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) c))))) (cbrt.f64 (/.f64 4 (*.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) c))))))
29.6b
(*.f64 -1/2 (*.f64 (/.f64 4 (*.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (cbrt.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))) (*.f64 1 (/.f64 c (cbrt.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))))
46.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
Compiler

Compiled 3458 to 1895 computations (45.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)))
1.3b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
20.3b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite121.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
8.3b
Rules
39×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64 times-frac_binary64
11×sqrt-prod_binary64
10×difference-of-squares_binary64
Counts
4 → 88
Calls

4 calls:

8.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
7.0ms
(-.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))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 2537 to 1439 computations (43.3% saved)

series275.0ms (4%)

Error
6.2b
Counts
4 → 82
Calls

4 calls:

76.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
66.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
52.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
43.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 4020 to 3030 computations (24.6% saved)

simplify149.0ms (2.2%)

Algorithm
egg-herbie
Rules
618×associate-/l*_binary64
527×associate-/r*_binary64
266×cancel-sign-sub-inv_binary64
195×distribute-rgt-neg-in_binary64
176×distribute-lft-neg-in_binary64
Counts
170 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02164261
15514033
216664004
349894004
449744004

prune67.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1052107
Fresh549
Picked011
Done011
Total1108118
Error
6.2b
Counts
118 → 8
Alt Table
StatusErrorProgram
46.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
46.5b
(*.f64 -1/2 (*.f64 2 (+.f64 (/.f64 c b) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))))
32.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
43.8b
(*.f64 -1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
29.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))
46.1b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (*.f64 (sqrt.f64 c) (/.f64 (sqrt.f64 c) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))))
46.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
40.6b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2)))))
Compiler

Compiled 1757 to 1099 computations (37.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2)))))
0.0b
(*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2))))

rewrite72.0ms (1%)

Algorithm
rewrite-expression-head
Error
6.2b
Rules
57×add-exp-log_binary64
38×prod-exp_binary64
36×add-cbrt-cube_binary64
21×cbrt-unprod_binary64
16×pow1_binary64
Counts
2 → 55
Calls

2 calls:

10.0ms
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2)))))
9.0ms
(*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2))))
Compiler

Compiled 970 to 800 computations (17.5% saved)

series33.0ms (0.5%)

Error
6.2b
Counts
2 → 12
Calls

2 calls:

15.0ms
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2)))))
15.0ms
(*.f64 4 (*.f64 1 (/.f64 c (*.f64 b 2))))
Compiler

Compiled 231 to 178 computations (22.9% saved)

simplify95.0ms (1.4%)

Algorithm
egg-herbie
Rules
857×times-frac_binary64
506×associate-*r/_binary64
440×associate-*l/_binary64
399×associate-/l*_binary64
298×associate-/r*_binary64
Counts
67 → 55
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0106896
1213680
2790527
33934527
44888527
54978527
64884527

prune29.0ms (0.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New49655
Fresh145
Picked101
Done022
Total511263
Error
6.2b
Counts
63 → 12
Alt Table
StatusErrorProgram
46.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
32.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
49.9b
(cbrt.f64 (pow.f64 (neg.f64 (/.f64 c b)) 3))
43.8b
(*.f64 -1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
29.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))
50.4b
(*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 2 (/.f64 c b))) (sqrt.f64 (*.f64 2 (/.f64 c b)))))
40.6b
(neg.f64 (/.f64 c b))
46.1b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (*.f64 (sqrt.f64 c) (/.f64 (sqrt.f64 c) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))))
41.0b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (/.f64 c b))) (cbrt.f64 (*.f64 2 (/.f64 c b)))) (cbrt.f64 (*.f64 2 (/.f64 c b)))))
51.3b
(exp.f64 (log.f64 (neg.f64 (/.f64 c b))))
46.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
51.1b
(*.f64 -1/2 (exp.f64 (log.f64 (*.f64 2 (/.f64 c b)))))
Compiler

Compiled 419 to 276 computations (34.1% saved)

regimes1.9s (27.6%)

Accuracy

Total 1.1b remaining (16.9%)

Threshold costs 0b (0%)

Compiler

Compiled 16032 to 10782 computations (32.7% saved)

bsearch69.0ms (1%)

Steps
ItersRangePoint
9
2.8681217371660862e+122
1.1170147148022088e+132
1.2458172873965611e+125
9
6.610131093643564e-292
7.140150232356879e-285
1.0118934187104876e-285
2
-8.915945153218393e+81
-6.011153247740761e+65
-8.049570799378294e+77
Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
043103
176103
296103
3120103
4139103
5147103
6150103
7146103

end2.0ms (0%)

Compiler

Compiled 72 to 49 computations (31.9% saved)

sample1.5s (21.4%)

Algorithm
intervals
Results
278.0ms1098×body2048valid
268.0ms5231×body128valid
141.0ms728×body1024valid
122.0ms400×body4096valid
52.0ms345×body512valid
34.0ms678×body128nan
21.0ms414×body128invalid
19.0ms198×body256valid
Compiler

Compiled 283 to 204 computations (27.9% saved)

Profiling

Loading profile data...