Details

Time bar (total: 18.9s)

analyze680.0ms (3.6%)

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)

sample128.0ms (0.7%)

Algorithm
intervals
Results
12.0ms181×body128valid
11.0ms37×body2048valid
5.0msbody4096valid
4.0ms15×body1024valid
2.0msbody512valid
1.0ms17×body128nan
1.0ms12×body128invalid
1.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify260.0ms (1.4%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
34.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
34.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
34.0b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series205.0ms (1.1%)

Counts
4 → 96
Calls

4 calls:

88.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
60.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
11.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite32.0ms (0.2%)

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:

9.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

simplify181.0ms (1%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
334×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
02434208
16953858
225123724
346943704
450313704

prune172.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1989207
Fresh011
Picked101
Done000
Total19910209
Error
5.7b
Counts
209 → 10
Alt Table
StatusErrorProgram
34.4b
(/.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)))))))
36.3b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
34.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
43.2b
(neg.f64 (/.f64 c b))
42.3b
(/.f64 (neg.f64 b) a)
40.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (+.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (*.f64 2 a))
40.1b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (/.f64 2 (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)))
34.1b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
41.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
Compiler

Compiled 5799 to 3387 computations (41.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series90.0ms (0.5%)

Counts
1 → 20
Calls

1 calls:

90.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite20.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
53×times-frac_binary64
37×*-un-lft-identity_binary64
22×add-exp-log_binary64
21×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64
Counts
1 → 74
Calls

1 calls:

10.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify103.0ms (0.5%)

Algorithm
egg-herbie
Rules
665×associate-/l*_binary64
599×div-sub_binary64
349×fma-def_binary64
295×fma-neg_binary64
265×associate-/r/_binary64
Counts
94 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01643247
14392847
215172670
345952670
461782670

prune223.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2552257
Fresh279
Picked011
Done000
Total25710267
Error
5.6b
Counts
267 → 10
Alt Table
StatusErrorProgram
34.4b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
40.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (+.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (*.f64 2 a))
36.8b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
41.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
42.3b
(/.f64 (neg.f64 b) a)
36.3b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
40.1b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (/.f64 2 (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)))
43.2b
(neg.f64 (/.f64 c b))
34.1b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
Compiler

Compiled 7966 to 4876 computations (38.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series87.0ms (0.5%)

Counts
1 → 20
Calls

1 calls:

87.0ms
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))

rewrite1.9s (10.2%)

Algorithm
rewrite-expression-head
Rules
10176×times-frac_binary64
6065×*-un-lft-identity_binary64
3797×add-sqr-sqrt_binary64
3797×add-cube-cbrt_binary64
2835×sqrt-prod_binary64
Counts
1 → 3009
Calls

1 calls:

76.0ms
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))

simplify4.6s (24.4%)

Algorithm
egg-herbie
Rules
881×associate-/r/_binary64
701×associate-/r*_binary64
615×associate-/l*_binary64
579×associate-/l/_binary64
125×times-frac_binary64
Counts
3029 → 1966
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0938281187
13033248447
25305248447

prune3.0s (16.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New224512246
Fresh268
Picked011
Done011
Total224792256
Error
5.6b
Counts
2256 → 9
Alt Table
StatusErrorProgram
36.8b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
41.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
42.3b
(/.f64 (neg.f64 b) a)
41.1b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))))) (*.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 c a) -4))) b))) (sqrt.f64 (+.f64 (fma.f64 b b (fma.f64 b b (*.f64 (*.f64 c a) -4))) (*.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 c a) -4))))))))
34.4b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
36.3b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
43.2b
(neg.f64 (/.f64 c b))
34.1b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
Compiler

Compiled 162716 to 97626 computations (40% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
2.6b
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
14.7b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series550.0ms (2.9%)

Counts
4 → 36
Calls

4 calls:

231.0ms
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
153.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
144.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
21.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite25.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
18×add-cube-cbrt_binary64
15×exp-sum_binary64
15×log-prod_binary64
Counts
4 → 100
Calls

4 calls:

6.0ms
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
3.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify117.0ms (0.6%)

Algorithm
egg-herbie
Rules
580×fma-def_binary64
348×fma-neg_binary64
342×associate-*l/_binary64
270×cancel-sign-sub-inv_binary64
178×associate-/l/_binary64
Counts
136 → 183
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02623659
15643335
220363189
348233189
448923189

prune152.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1821183
Fresh066
Picked101
Done022
Total1839192
Error
3.3b
Counts
192 → 9
Alt Table
StatusErrorProgram
48.6b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b))) (*.f64 2 a))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
36.8b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
41.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
42.3b
(/.f64 (neg.f64 b) a)
41.1b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))))) (*.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 c a) -4))) b))) (sqrt.f64 (+.f64 (fma.f64 b b (fma.f64 b b (*.f64 (*.f64 c a) -4))) (*.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 c a) -4))))))))
34.4b
(/.f64 (/.f64 1 (/.f64 2 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) (/.f64 a (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
43.2b
(neg.f64 (/.f64 c b))
34.1b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
Compiler

Compiled 5342 to 3504 computations (34.4% saved)

regimes4.2s (22.3%)

Accuracy

Total 7.9b remaining (70.9%)

Threshold costs 0b (0%)

Counts
305 → 3
Compiler

Compiled 41326 to 28350 computations (31.4% saved)

bsearch79.0ms (0.4%)

Steps
ItersRangePoint
10
8.978518197639981e-169
6.284943703071234e-159
6.212289707649754e-159
6
-6.856485632986412e+110
-2.429146751354077e+106
-2.284455722178938e+110
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
02954
14952
27452
38652
49252
59352
69052

end1.0ms (0%)

Compiler

Compiled 38 to 23 computations (39.5% saved)

sample2.0s (10.3%)

Algorithm
intervals
Results
438.0ms1145×body2048valid
430.0ms5217×body128valid
192.0ms716×body1024valid
157.0ms393×body4096valid
76.0ms606×body128nan
73.0ms370×body512valid
27.0ms362×body128invalid
22.0ms159×body256valid
Compiler

Compiled 281 to 189 computations (32.7% saved)

Profiling

Loading profile data...