Details

Time bar (total: 7.2s)

analyze733.0ms (10.1%)

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)

sample2.5s (34.8%)

Results
792.0ms5399×body128valid
686.0ms1193×body2048valid
340.0ms743×body1024valid
272.0ms401×body4096valid
161.0ms1145×body128invalid
129.0ms370×body512valid
37.0ms150×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify259.0ms (3.6%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
33.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
34.0b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
34.0b
(*.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)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 4 a) c)
0.5b
(+.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))
22.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series81.0ms (1.1%)

Counts
4 → 100
Calls

4 calls:

37.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
28.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
10.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
6.0ms
(*.f64 (*.f64 4 a) c)

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
10×fma-def_binary64
10×add-sqr-sqrt_binary64
10×add-log-exp_binary64
10×pow1_binary64
Counts
4 → 80
Calls

4 calls:

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

simplify117.0ms (1.6%)

Algorithm
egg-herbie
Rules
708×fma-def_binary64
604×fma-neg_binary64
312×cancel-sign-sub-inv_binary64
230×distribute-rgt-neg-in_binary64
199×distribute-lft-neg-in_binary64
Counts
180 → 168
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01962932
15212807
218192667
344482663
449942663
549162663

prune141.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15810168
Fresh011
Picked101
Done000
Total15911170
Error
11.8b
Counts
170 → 11
Alt Table
StatusErrorProgram
34.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
37.3b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a))
34.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
47.2b
(/.f64 (*.f64 -2 b) (*.f64 2 a))
47.9b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
44.4b
(/.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (*.f64 2 a))
35.9b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
55.5b
(/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (*.f64 b b) 3) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.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))
56.0b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
34.0b
(/.f64 (*.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a))
36.3b
(/.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 4667 to 2739 computations (41.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 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
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.5b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
22.2b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series134.0ms (1.9%)

Counts
4 → 96
Calls

4 calls:

58.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
38.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
28.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite24.0ms (0.3%)

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:

11.0ms
(*.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))

simplify186.0ms (2.6%)

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

prune173.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2247231
Fresh7310
Picked011
Done000
Total23111242
Error
7.2b
Counts
242 → 11
Alt Table
StatusErrorProgram
34.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
35.8b
(*.f64 (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))
36.3b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
31.7b
(/.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))
47.7b
(-.f64 (/.f64 c b) (/.f64 b a))
34.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
47.2b
(/.f64 (*.f64 -2 b) (*.f64 2 a))
39.2b
(neg.f64 (/.f64 c b))
34.7b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
35.9b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
34.0b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b)) a)
Compiler

Compiled 6427 to 3774 computations (41.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.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))
0.9b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
13.5b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
22.2b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series174.0ms (2.4%)

Counts
3 → 64
Calls

3 calls:

137.0ms
(/.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))
33.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
4.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite32.0ms (0.4%)

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:

13.0ms
(/.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)

simplify110.0ms (1.5%)

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

prune192.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2382240
Fresh279
Picked101
Done011
Total24110251
Error
7.2b
Counts
251 → 10
Alt Table
StatusErrorProgram
39.2b
(neg.f64 (/.f64 c b))
33.5b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (exp.f64 (log.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
36.3b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
29.1b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
47.7b
(-.f64 (/.f64 c b) (/.f64 b a))
47.2b
(/.f64 (*.f64 -2 b) (*.f64 2 a))
34.7b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
35.9b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
34.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
34.0b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b)) a)
Compiler

Compiled 8095 to 5126 computations (36.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.4b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.9b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
22.2b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series129.0ms (1.8%)

Counts
1 → 20
Calls

1 calls:

129.0ms
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
associate-/r*_binary64
times-frac_binary64
Counts
1 → 27
Calls

1 calls:

6.0ms
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

simplify63.0ms (0.9%)

Algorithm
egg-herbie
Rules
769×times-frac_binary64
615×associate-/l*_binary64
357×associate-/r*_binary64
352×fma-neg_binary64
235×fma-def_binary64
Counts
47 → 67
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01271488
13661333
211801254
348441254
450781254

prune141.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1832185
Fresh088
Picked011
Done011
Total18312195
Error
7.2b
Counts
195 → 12
Alt Table
StatusErrorProgram
35.6b
(/.f64 (*.f64 -2 c) (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
47.2b
(/.f64 (*.f64 -2 b) (*.f64 2 a))
39.2b
(neg.f64 (/.f64 c b))
33.5b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (exp.f64 (log.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
49.5b
(exp.f64 (-.f64 (log.f64 (*.f64 -2 c)) (log.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
34.0b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b)) a)
36.3b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
29.1b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
47.7b
(-.f64 (/.f64 c b) (/.f64 b a))
34.7b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
35.9b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
34.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
Compiler

Compiled 4731 to 2861 computations (39.5% saved)

regimes1.6s (22.6%)

Accuracy

Total 1.4b remaining (20%)

Threshold costs 0b (0%)

Counts
142 → 4
Compiler

Compiled 13224 to 9138 computations (30.9% saved)

bsearch143.0ms (2%)

Steps
ItersRangePoint
9
1.2809204955329581e+33
1.3069589410673845e+38
1.2931991447555657e+38
10
-6.308315690216156e-274
-3.9360892857913695e-285
-1.7696545692563913e-275
8
-1.761622937979916e+128
-7.291574701407998e+119
-1.3104263752164671e+126
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03174
14674
25574
36174
46374
56374

end166.0ms (2.3%)

Compiler

Compiled 328 to 223 computations (32% saved)

Profiling

Loading profile data...