Details

Time bar (total: 8.7s)

analyze1.3s (14.6%)

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)

sample85.0ms (1%)

Algorithm
intervals
Results
20.0ms175×body128valid
17.0ms30×body2048valid
10.0ms23×body1024valid
8.0ms11×body4096valid
3.0ms29×body128nan
3.0msbody512valid
2.0msbody256valid
1.0ms11×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify184.0ms (2.1%)

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 → 1
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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
32.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
32.4b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
Compiler

Compiled 54 to 36 computations (33.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
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))))
21.6b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite905.0ms (10.4%)

Algorithm
rewrite-expression-head
Error
32.2b
Rules
25×*-un-lft-identity_binary64
16×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
12×times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 77
Calls

4 calls:

10.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
8.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
2.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
1.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))
Compiler

Compiled 1782 to 979 computations (45.1% saved)

series178.0ms (2.1%)

Error
5.4b
Counts
4 → 78
Calls

4 calls:

48.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
42.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
37.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
26.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))
Compiler

Compiled 3315 to 2387 computations (28% saved)

simplify107.0ms (1.2%)

Algorithm
egg-herbie
Rules
710×times-frac_binary64
442×associate-/l*_binary64
430×associate-/r*_binary64
353×fma-def_binary64
175×fma-neg_binary64
Counts
155 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01843090
14642911
213172783
348472783
449882783

prune85.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New11415129
Fresh000
Picked101
Done000
Total11515130
Error
7.6b
Counts
130 → 15
Alt Table
StatusErrorProgram
48.4b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))) a) 3)))
43.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
43.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
50.9b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
50.1b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
31.7b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
32.8b
(*.f64 -1/2 (/.f64 (+.f64 b (*.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))))))) a))
33.7b
(*.f64 -1/2 (/.f64 (+.f64 b (*.f64 (*.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) a))
44.4b
(*.f64 -1/2 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) a))
46.6b
(*.f64 -1/2 (*.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
57.9b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
49.8b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (*.f64 b b))) a))
36.3b
(*.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) a))
32.2b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a)))
32.4b
(*.f64 -1/2 (/.f64 (+.f64 b (*.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) a))
Compiler

Compiled 2421 to 1557 computations (35.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
0.2b
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
0.5b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))
13.1b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite153.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
4.8b
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:

8.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
4.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
3.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))
Compiler

Compiled 4311 to 2956 computations (31.4% saved)

series234.0ms (2.7%)

Error
7.4b
Counts
4 → 51
Calls

4 calls:

80.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
69.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
54.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))
10.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
Compiler

Compiled 3355 to 2535 computations (24.4% saved)

simplify179.0ms (2.1%)

Algorithm
egg-herbie
Rules
471×associate-*l/_binary64
410×associate-*r/_binary64
393×associate-/r/_binary64
312×fma-def_binary64
277×fma-neg_binary64
Counts
215 → 182
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02536039
15725542
218515398
347195398
449465398

prune95.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1766182
Fresh8614
Picked101
Done000
Total18512197
Error
5.3b
Counts
197 → 12
Alt Table
StatusErrorProgram
48.4b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))) a) 3)))
43.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
42.2b
(*.f64 -1/2 (*.f64 -1/2 (/.f64 (*.f64 c -4) b)))
49.8b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (*.f64 b b))) a))
31.7b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.8b
(*.f64 -1/2 (/.f64 (+.f64 b (*.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))))))) a))
31.7b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) -1))
31.6b
(*.f64 -1/2 (*.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)))
43.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
50.1b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
36.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) 3)))))))
42.1b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 c -4)) -2))))
Compiler

Compiled 3256 to 2049 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 -4 (*.f64 c a))
0.1b
(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)
0.5b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
13.1b
(sqrt.f64 (*.f64 -4 (*.f64 c a)))

rewrite76.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
25×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
15×pow1_binary64
12×times-frac_binary64
Counts
4 → 86
Calls

4 calls:

4.0ms
(*.f64 -4 (*.f64 c a))
4.0ms
(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)
3.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
3.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
Compiler

Compiled 1886 to 1178 computations (37.5% saved)

series155.0ms (1.8%)

Error
5.3b
Counts
4 → 42
Calls

4 calls:

70.0ms
(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)
52.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
10.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
10.0ms
(*.f64 -4 (*.f64 c a))
Compiler

Compiled 2517 to 1911 computations (24.1% saved)

simplify78.0ms (0.9%)

Algorithm
egg-herbie
Rules
729×associate-*l*_binary64
678×associate-/l*_binary64
551×associate-/r*_binary64
219×fma-def_binary64
179×associate-*l/_binary64
Counts
128 → 47
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992467
14682293
213562231
350742231

prune37.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New46147
Fresh11011
Picked011
Done000
Total471259
Error
5.3b
Counts
59 → 12
Alt Table
StatusErrorProgram
42.2b
(*.f64 -1/2 (*.f64 -1/2 (/.f64 (*.f64 c -4) b)))
49.8b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (*.f64 b b))) a))
31.7b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.8b
(*.f64 -1/2 (/.f64 (+.f64 b (*.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))))))) a))
31.7b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) -1))
43.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
31.8b
(*.f64 -1/2 (*.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 -4) (cbrt.f64 -4)) (*.f64 (*.f64 c a) (cbrt.f64 -4)))))) a)))
31.6b
(*.f64 -1/2 (*.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)))
43.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
50.1b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
36.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) 3)))))))
42.1b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 c -4)) -2))))
Compiler

Compiled 1172 to 791 computations (32.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 -4 (*.f64 c a))
0.2b
(*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))
0.5b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
13.1b
(sqrt.f64 (*.f64 -4 (*.f64 c a)))

rewrite85.0ms (1%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
21×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
18×add-exp-log_binary64
17×pow1_binary64
16×associate-*l*_binary64
Counts
4 → 95
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))
4.0ms
(*.f64 -4 (*.f64 c a))
3.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
2.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
Compiler

Compiled 2145 to 1363 computations (36.5% saved)

series153.0ms (1.8%)

Error
5.3b
Counts
4 → 42
Calls

4 calls:

65.0ms
(*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))))
53.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))
11.0ms
(*.f64 -4 (*.f64 c a))
11.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
Compiler

Compiled 2465 to 1855 computations (24.7% saved)

simplify77.0ms (0.9%)

Algorithm
egg-herbie
Rules
747×associate-/l*_binary64
633×associate-/r*_binary64
341×fma-def_binary64
242×distribute-rgt-in_binary64
234×distribute-lft-in_binary64
Counts
137 → 80
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02112612
15492371
216472311
352052311

prune49.0ms (0.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New80080
Fresh01010
Picked011
Done011
Total801292
Error
5.3b
Counts
92 → 12
Alt Table
StatusErrorProgram
42.2b
(*.f64 -1/2 (*.f64 -1/2 (/.f64 (*.f64 c -4) b)))
49.8b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (*.f64 b b))) a))
31.7b
(*.f64 -1/2 (*.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a)))))))
32.8b
(*.f64 -1/2 (/.f64 (+.f64 b (*.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))))))) a))
31.7b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) -1))
43.2b
(*.f64 -1/2 (/.f64 (*.f64 b 2) a))
31.8b
(*.f64 -1/2 (*.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 -4) (cbrt.f64 -4)) (*.f64 (*.f64 c a) (cbrt.f64 -4)))))) a)))
31.6b
(*.f64 -1/2 (*.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 c a))))) a)))
43.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
50.1b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
36.2b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) 3)))))))
42.1b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 c -4)) -2))))
Compiler

Compiled 1549 to 975 computations (37.1% saved)

regimes2.7s (31.3%)

Accuracy

Total 4.6b remaining (44.8%)

Threshold costs 0b (0%)

Compiler

Compiled 16208 to 11358 computations (29.9% saved)

bsearch68.0ms (0.8%)

Steps
ItersRangePoint
10
5.747738448649357e+78
2.1698839341732341e+99
8.470534450340484e+97
8
-8.635924748638075e-49
-1.5289181739433208e-52
-2.5636004990570266e-52
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02959
13959
23959

end1.0ms (0%)

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.7s (19.1%)

Algorithm
intervals
Results
350.0ms5210×body128valid
347.0ms1109×body2048valid
180.0ms729×body1024valid
151.0ms405×body4096valid
65.0ms372×body512valid
41.0ms683×body128nan
23.0ms370×body128invalid
21.0ms175×body256valid
Compiler

Compiled 302 to 223 computations (26.2% saved)

Profiling

Loading profile data...