Details

Time bar (total: 8.1s)

analyze637.0ms (7.9%)

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)

sample2.8s (34.7%)

Results
1.1s5359×body128valid
664.0ms1158×body2048valid
318.0ms739×body1024valid
266.0ms431×body4096valid
146.0ms1093×body128invalid
133.0ms389×body512valid
46.0ms180×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify145.0ms (1.8%)

Algorithm
egg-herbie
Rules
2079×fma-neg_binary64
1006×fma-def_binary64
919×div-sub_binary64
626×distribute-rgt-in_binary64
435×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01526
13824
29524
322722
435722
561422
6110322
7137322
8163622
9233022
10318722
11288022
12282722
13289622
14292222
15379722
16482422
17524022

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
34.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.0b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
Compiler

Compiled 71 to 46 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
0.9b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
23.8b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series106.0ms (1.3%)

Counts
3 → 60
Calls

3 calls:

43.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
35.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
28.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
distribute-lft-out_binary64
Counts
3 → 67
Calls

3 calls:

5.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
3.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Rules
820×times-frac_binary64
539×associate-/l*_binary64
458×fma-def_binary64
246×fma-neg_binary64
189×cancel-sign-sub-inv_binary64
Counts
127 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01883311
15103170
215343008
348403008
449543008

prune155.0ms (1.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New15613169
Fresh000
Picked011
Done000
Total15614170
Error
7.6b
Counts
170 → 14
Alt Table
StatusErrorProgram
56.5b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
37.8b
(*.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))) a))
32.5b
(*.f64 -1/2 (*.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a)))
43.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
50.1b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (sqrt.f64 a)) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (sqrt.f64 a))))
34.0b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
32.8b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (cbrt.f64 a))))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
48.2b
(*.f64 -1/2 (*.f64 (sqrt.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a)) (sqrt.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a))))
43.2b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
32.4b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
49.1b
(*.f64 -1/2 (exp.f64 (log.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a))))
45.4b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
34.5b
(*.f64 -1/2 (/.f64 (+.f64 b (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
Compiler

Compiled 4970 to 3026 computations (39.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
0.1b
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
0.2b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
16.6b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series415.0ms (5.1%)

Counts
4 → 42
Calls

4 calls:

183.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
136.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
82.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
14.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
114×times-frac_binary64
99×*-un-lft-identity_binary64
65×add-sqr-sqrt_binary64
65×add-cube-cbrt_binary64
22×associate-/r*_binary64
Counts
4 → 164
Calls

4 calls:

7.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
3.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
3.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))
2.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))

simplify162.0ms (2%)

Algorithm
egg-herbie
Rules
502×associate-*l/_binary64
496×fma-def_binary64
478×fma-neg_binary64
422×associate-/r/_binary64
308×cancel-sign-sub-inv_binary64
Counts
206 → 291
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02616252
16445816
221635690
349385684
451875684

prune272.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2856291
Fresh8412
Picked101
Done011
Total29411305
Error
4.4b
Counts
305 → 11
Alt Table
StatusErrorProgram
32.4b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.4b
(*.f64 -1/2 (/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
43.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.0b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
48.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
43.2b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
32.4b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
32.5b
(*.f64 -1/2 (/.f64 1 (/.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))) (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
45.4b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
43.6b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
Compiler

Compiled 9123 to 6038 computations (33.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
0.2b
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
0.2b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
16.6b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series289.0ms (3.6%)

Counts
2 → 28
Calls

2 calls:

172.0ms
(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
115.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

rewrite75.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
585×times-frac_binary64
348×*-un-lft-identity_binary64
256×add-sqr-sqrt_binary64
256×add-cube-cbrt_binary64
46×distribute-lft-out_binary64
Counts
2 → 338
Calls

2 calls:

11.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
4.0ms
(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))

simplify383.0ms (4.7%)

Algorithm
egg-herbie
Rules
651×associate-/l*_binary64
385×fma-def_binary64
322×associate-/l/_binary64
236×associate-/r/_binary64
211×distribute-rgt-in_binary64
Counts
366 → 395
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026814663
171113409
2212213279
3466113275
4499813275
5494213275

prune410.0ms (5.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New4622464
Fresh099
Picked101
Done011
Total46312475
Error
4.3b
Counts
475 → 12
Alt Table
StatusErrorProgram
32.4b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.4b
(*.f64 -1/2 (/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
49.7b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (fma.f64 (/.f64 b (*.f64 -4 (*.f64 a c))) -2 (/.f64 -1/2 b))))
48.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
43.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.0b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
43.2b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
48.2b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))))))
32.5b
(*.f64 -1/2 (/.f64 1 (/.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))) (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
45.4b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
43.6b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
Compiler

Compiled 16956 to 11874 computations (30% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
0.1b
(/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
0.2b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
16.6b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series293.0ms (3.6%)

Counts
2 → 28
Calls

2 calls:

183.0ms
(*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
110.0ms
(/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×add-exp-log_binary64
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
18×associate-*r*_binary64
18×div-exp_binary64
Counts
2 → 85
Calls

2 calls:

8.0ms
(*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
8.0ms
(/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))

simplify90.0ms (1.1%)

Algorithm
egg-herbie
Rules
696×fma-neg_binary64
329×associate-*l/_binary64
305×fma-def_binary64
285×associate-*r/_binary64
227×sub-neg_binary64
Counts
113 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01993082
15222599
217822579
340022575
449492575

prune178.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2300230
Fresh01010
Picked011
Done011
Total23012242
Error
4.3b
Counts
242 → 12
Alt Table
StatusErrorProgram
32.4b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.4b
(*.f64 -1/2 (/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
49.7b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (fma.f64 (/.f64 b (*.f64 -4 (*.f64 a c))) -2 (/.f64 -1/2 b))))
48.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
43.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.0b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
43.2b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
48.2b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))))))
32.5b
(*.f64 -1/2 (/.f64 1 (/.f64 (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))) (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
45.4b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
43.6b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
Compiler

Compiled 6816 to 4661 computations (31.6% saved)

regimes1.2s (15%)

Accuracy

Total 7.6b remaining (72.9%)

Threshold costs 0b (0%)

Counts
122 → 3
Compiler

Compiled 11568 to 8134 computations (29.7% saved)

bsearch71.0ms (0.9%)

Steps
ItersRangePoint
7
3.752089695048035e+93
8.567713446312838e+95
5.799761191344333e+95
7
-4.340950814285089e-30
-1.3387037076683125e-31
-1.5513227110811959e-31
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
02860
13760
24460
34860
45160
55260
65260

end164.0ms (2%)

Compiler

Compiled 324 to 229 computations (29.3% saved)

Profiling

Loading profile data...