Details

Time bar (total: 10.6s)

analyze629.0ms (5.9%)

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)

sample135.0ms (1.3%)

Algorithm
intervals
Results
12.0ms36×body2048valid
11.0ms163×body128valid
6.0ms16×body4096valid
6.0ms22×body1024valid
2.0ms12×body512valid
1.0ms20×body128nan
1.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify397.0ms (3.8%)

Algorithm
egg-herbie
Rules
2009×fma-neg_binary64
1508×div-sub_binary64
1334×associate-/l*_binary64
1156×fma-def_binary64
685×associate-/l/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13422
26422
313222
419822
532522
655222
791822
8135222
9155422
10235922
11315822
12256522
13265322
14321922
15336122
16346122
17398522
18417122
19443922
20465922
21470122
22475722
23494122
24494122
25336522
26305922
27298322
28298522
29299722
30299722
31299722
32299722
33273622

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
36.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
36.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
37.0b
(*.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)

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 4 (*.f64 a c))))) (*.f64 2 a))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.5b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
24.3b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series189.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

83.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
53.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
42.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
10.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

rewrite27.0ms (0.3%)

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 4 (*.f64 a c))))) (*.f64 2 a))
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
3.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

simplify122.0ms (1.2%)

Algorithm
egg-herbie
Rules
697×fma-neg_binary64
327×cancel-sign-sub-inv_binary64
226×distribute-rgt-neg-in_binary64
150×distribute-rgt-neg-out_binary64
146×associate-*r*_binary64
Counts
186 → 207
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434202
16933825
224883724
346523704
449853704

prune165.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New19710207
Fresh011
Picked101
Done000
Total19811209
Error
9.1b
Counts
209 → 11
Alt Table
StatusErrorProgram
37.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
41.9b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.7b
(-.f64 (/.f64 c b) (/.f64 b a))
49.4b
(/.f64 (/.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 2 a))
44.5b
(/.f64 (neg.f64 b) a)
38.9b
(neg.f64 (/.f64 c b))
38.4b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
39.8b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
48.7b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
37.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
48.5b
(/.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
Compiler

Compiled 5735 to 3208 computations (44.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
1.5b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
24.3b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series189.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

82.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
52.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
45.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
4 → 109
Calls

4 calls:

9.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

simplify194.0ms (1.8%)

Algorithm
egg-herbie
Rules
527×fma-neg_binary64
338×distribute-rgt-in_binary64
273×cancel-sign-sub-inv_binary64
155×associate-*l*_binary64
153×associate-*r*_binary64
Counts
205 → 231
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02675424
16734468
225244293
345504293
449914293
549944293
648844293

prune157.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2265231
Fresh4610
Picked011
Done000
Total23012242
Error
9.1b
Counts
242 → 12
Alt Table
StatusErrorProgram
37.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
41.9b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.7b
(-.f64 (/.f64 c b) (/.f64 b a))
38.9b
(neg.f64 (/.f64 c b))
44.6b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
48.7b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
37.1b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
44.5b
(/.f64 (neg.f64 b) a)
43.5b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 c (*.f64 a -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
37.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
39.8b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
58.7b
(*.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (neg.f64 (*.f64 (sqrt.f64 b) (sqrt.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) (*.f64 (sqrt.f64 b) (sqrt.f64 b)))) (/.f64 1/2 a))
Compiler

Compiled 6437 to 3768 computations (41.5% saved)

localize11.0ms (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 4 (*.f64 a c)))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.5b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
24.3b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series85.0ms (0.8%)

Counts
1 → 20
Calls

1 calls:

85.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

rewrite19.0ms (0.2%)

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:

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

simplify103.0ms (1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
01643247
14342847
215122670
345872670
461712670

prune189.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2552257
Fresh3710
Picked011
Done011
Total25811269
Error
9.1b
Counts
269 → 11
Alt Table
StatusErrorProgram
37.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
41.9b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.7b
(-.f64 (/.f64 c b) (/.f64 b a))
44.6b
(/.f64 1 (/.f64 (*.f64 2 a) (*.f64 b -2)))
38.9b
(neg.f64 (/.f64 c b))
37.1b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
43.5b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 c (*.f64 a -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
48.8b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (*.f64 b b)))))
37.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
39.8b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
58.7b
(*.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (neg.f64 (*.f64 (sqrt.f64 b) (sqrt.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) (*.f64 (sqrt.f64 b) (sqrt.f64 b)))) (/.f64 1/2 a))
Compiler

Compiled 7886 to 4609 computations (41.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.3b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
18.1b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
24.3b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series315.0ms (3%)

Counts
3 → 64
Calls

3 calls:

262.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
50.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
3.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite30.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
15×add-cube-cbrt_binary64
Counts
3 → 92
Calls

3 calls:

11.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
9.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

simplify113.0ms (1.1%)

Algorithm
egg-herbie
Rules
616×fma-neg_binary64
248×associate-*l*_binary64
225×associate-/l*_binary64
220×associate-*r*_binary64
176×div-sub_binary64
Counts
156 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503787
17083244
231323157
346133157
449323157

prune166.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2391240
Fresh358
Picked101
Done112
Total2447251
Error
9.1b
Counts
251 → 7
Alt Table
StatusErrorProgram
37.1b
(/.f64 (/.f64 (*.f64 (*.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
48.8b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (*.f64 b b)))))
44.6b
(/.f64 1 (/.f64 (*.f64 2 a) (*.f64 b -2)))
44.7b
(-.f64 (/.f64 c b) (/.f64 b a))
38.9b
(neg.f64 (/.f64 c b))
37.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
39.8b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
Compiler

Compiled 7853 to 4955 computations (36.9% saved)

regimes3.1s (28.9%)

Accuracy

Total 1.5b remaining (22.1%)

Threshold costs 0b (0%)

Counts
148 → 4
Compiler

Compiled 12444 to 8724 computations (29.9% saved)

bsearch102.0ms (1%)

Steps
ItersRangePoint
1
6.762108974156066e+97
8.581797180489703e+110
2.4411469808920094e+104
8
-2.512532013418455e-158
-7.121325756367925e-161
-1.3734960260801592e-159
5
-1.8293729419057588e+22
-9.130147825656278e+21
-1.8145633063846896e+22
Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03782
15880
27580
39080
49780
510080
610180
710080

end2.0ms (0%)

Compiler

Compiled 57 to 34 computations (40.4% saved)

sample4.1s (38.8%)

Algorithm
intervals
Results
1.5s5198×body128valid
697.0ms1083×body2048valid
420.0ms761×body1024valid
321.0ms389×body4096valid
148.0ms384×body512valid
84.0ms690×body128nan
52.0ms420×body128invalid
52.0ms185×body256valid
Compiler

Compiled 185 to 125 computations (32.4% saved)

Profiling

Loading profile data...