Details

Time bar (total: 9.9s)

analyze1.0s (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)

sample2.6s (25.9%)

Results
704.0ms5358×body128valid
617.0ms1151×body2048valid
400.0ms432×body4096valid
324.0ms768×body1024valid
149.0ms1108×body128invalid
120.0ms373×body512valid
38.0ms174×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify260.0ms (2.6%)

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
32.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
32.7b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
32.6b
(/.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
0.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series181.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

80.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
49.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
41.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
10.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite29.0ms (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 (*.f64 4 a) c)))) (*.f64 2 a))
7.0ms
(+.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))

simplify119.0ms (1.2%)

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
02434216
16953858
225123724
346943704
450313704

prune144.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1989207
Fresh011
Picked101
Done000
Total19910209
Error
4.9b
Counts
209 → 10
Alt Table
StatusErrorProgram
32.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
36.0b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
45.6b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.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))))))))
42.0b
(/.f64 (-.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) (*.f64 2 a))
32.8b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
46.9b
(/.f64 (neg.f64 b) a)
47.0b
(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
32.7b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
39.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 5705 to 3333 computations (41.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
0.2b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
21.7b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series170.0ms (1.7%)

Counts
3 → 60
Calls

3 calls:

80.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
50.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
40.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
3 → 99
Calls

3 calls:

8.0ms
(*.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)))

simplify140.0ms (1.4%)

Algorithm
egg-herbie
Rules
505×fma-neg_binary64
316×distribute-rgt-in_binary64
279×distribute-lft-in_binary64
261×cancel-sign-sub-inv_binary64
151×associate-*r*_binary64
Counts
159 → 207
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02584859
16623980
224793807
348593807
449663807

prune412.0ms (4.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2043207
Fresh279
Picked011
Done000
Total20611217
Error
4.9b
Counts
217 → 11
Alt Table
StatusErrorProgram
32.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
36.0b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
35.5b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 a (*.f64 c -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
47.0b
(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
41.2b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
46.9b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
32.7b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.6b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.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))))))))
46.9b
(/.f64 (neg.f64 b) a)
39.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 5950 to 3474 computations (41.6% saved)

localize78.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.6b
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
2.6b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
6.7b
(/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))
12.2b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series1.2s (12.6%)

Counts
4 → 42
Calls

4 calls:

572.0ms
(/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))
465.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
181.0ms
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
23.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite43.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity_binary64
45×add-cbrt-cube_binary64
45×add-exp-log_binary64
43×add-sqr-sqrt_binary64
33×add-cube-cbrt_binary64
Counts
4 → 162
Calls

4 calls:

11.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
7.0ms
(/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))
5.0ms
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify203.0ms (2.1%)

Algorithm
egg-herbie
Rules
421×times-frac_binary64
385×fma-neg_binary64
307×associate-/l*_binary64
271×associate-/r*_binary64
232×associate-*r*_binary64
Counts
204 → 295
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03777962
19846021
242605997
350405997

prune250.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2941295
Fresh189
Picked011
Done011
Total29511306
Error
4.9b
Counts
306 → 11
Alt Table
StatusErrorProgram
32.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
36.0b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
35.5b
(/.f64 (*.f64 4 (*.f64 c a)) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
47.0b
(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
41.2b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
46.9b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
32.7b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.6b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.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))))))))
46.9b
(/.f64 (neg.f64 b) a)
39.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 11482 to 6826 computations (40.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))
1.6b
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
11.8b
(/.f64 (*.f64 4 (*.f64 c a)) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
12.2b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series662.0ms (6.7%)

Counts
2 → 28
Calls

2 calls:

475.0ms
(/.f64 (*.f64 4 (*.f64 c a)) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
187.0ms
(*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))

rewrite40.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
60×prod-diff_binary64
47×*-un-lft-identity_binary64
45×add-sqr-sqrt_binary64
43×add-cube-cbrt_binary64
43×add-cbrt-cube_binary64
Counts
2 → 128
Calls

2 calls:

11.0ms
(/.f64 (*.f64 4 (*.f64 c a)) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
9.0ms
(*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))

simplify173.0ms (1.7%)

Algorithm
egg-herbie
Rules
606×fma-def_binary64
561×times-frac_binary64
328×associate-*l*_binary64
316×associate-*r*_binary64
259×associate-/l*_binary64
Counts
156 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03367183
18455503
239165487
348085487
449755487

prune280.0ms (2.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New3150315
Fresh088
Picked011
Done022
Total31511326
Error
4.9b
Counts
326 → 11
Alt Table
StatusErrorProgram
32.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
36.0b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
35.5b
(/.f64 (*.f64 4 (*.f64 c a)) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
47.0b
(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
41.2b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
46.9b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
32.7b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.6b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.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))))))))
46.9b
(/.f64 (neg.f64 b) a)
39.9b
(neg.f64 (/.f64 c b))
Compiler

Compiled 14329 to 8886 computations (38% saved)

regimes1.5s (15.4%)

Accuracy

Total 3.4b remaining (37.2%)

Threshold costs 0b (0%)

Counts
120 → 4
Compiler

Compiled 14144 to 9480 computations (33% saved)

bsearch133.0ms (1.3%)

Steps
ItersRangePoint
8
1.2172116468797495e+31
3.416069190654851e+35
1.6817334037718362e+33
9
3.530460311750897e-163
2.9360496468858698e-154
5.718942250318738e-161
9
-3.9717383279087257e+68
-2.802707603230092e+63
-1.6023237827264455e+68
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
04191
16489
28889
310089
410689
510789
610689

end147.0ms (1.5%)

Compiler

Compiled 346 to 225 computations (35% saved)

Profiling

Loading profile data...