Details

Time bar (total: 10.9s)

analyze658.0ms (6.1%)

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
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (22.5%)

Results
749.0ms5358×body128valid
635.0ms1149×body2048valid
370.0ms790×body1024valid
315.0ms419×body4096valid
141.0ms1124×body128invalid
119.0ms365×body512valid
50.0ms175×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify34.0ms (0.3%)

Algorithm
egg-herbie
Rules
1220×fma-neg_binary64
367×fma-def_binary64
351×times-frac_binary64
266×associate-/l*_binary64
254×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01326
13022
26922
316022
426422
543322
674422
7134122
8276922
9470222
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
32.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
32.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 3 a) c)
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
0.8b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

series121.0ms (1.1%)

Counts
4 → 84
Calls

4 calls:

52.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
38.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
27.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
4.0ms
(*.f64 (*.f64 3 a) c)

rewrite69.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
248×expm1-udef_binary64
248×log1p-udef_binary64
150×add-sqr-sqrt_binary64
145×log1p-expm1-u_binary64
145×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01368
130258
2445158
Stop Event
node limit
Counts
4 → 117
Calls

4 calls:

67.0ms
(*.f64 (*.f64 3 a) c)
67.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
67.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
67.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

simplify48.0ms (0.4%)

Algorithm
egg-herbie
Rules
766×times-frac_binary64
487×associate-/l*_binary64
403×associate-/r*_binary64
385×fma-def_binary64
136×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01342091
14232069
214552028
Stop Event
node limit
Counts
201 → 187

prune185.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New17611187
Fresh011
Picked101
Done000
Total17712189
Error
5.6b
Counts
189 → 12
Alt Table
StatusErrorProgram
45.2b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
34.5b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))) 1/4) 2)) (*.f64 3 a))
43.1b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
45.6b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
55.7b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
46.5b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (/.f64 1/3 a)))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
32.9b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
39.2b
(*.f64 (/.f64 -1/2 b) c)
39.1b
(*.f64 -1/2 (/.f64 c b))
45.9b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
46.1b
(/.f64 (+.f64 (neg.f64 b) (-.f64 (*.f64 3/2 (*.f64 (/.f64 a b) c)) b)) (*.f64 3 a))
Compiler

Compiled 4907 to 3096 computations (36.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
0.4b
(/.f64 1/3 a)
0.8b
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b)
21.7b
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3))))

series114.0ms (1%)

Counts
4 → 60
Calls

4 calls:

51.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
34.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b)
27.0ms
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3))))
1.0ms
(/.f64 1/3 a)

rewrite72.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
737×prod-diff_binary64
152×egg-rr
140×add-sqr-sqrt_binary64
133×log1p-expm1-u_binary64
133×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01355
128252
2364652
Stop Event
node limit
Counts
4 → 152
Calls

4 calls:

67.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
67.0ms
(/.f64 1/3 a)
67.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b)
67.0ms
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3))))

simplify44.0ms (0.4%)

Algorithm
egg-herbie
Rules
766×times-frac_binary64
487×associate-/l*_binary64
403×associate-/r*_binary64
385×fma-def_binary64
136×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01341923
14231901
214551860
Stop Event
node limit
Counts
212 → 221

prune186.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2156221
Fresh5611
Picked011
Done000
Total22013233
Error
5.6b
Counts
233 → 13
Alt Table
StatusErrorProgram
45.3b
(*.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (/.f64 1/3 a))
55.7b
(*.f64 (-.f64 b b) (/.f64 1/3 a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
33.4b
(/.f64 (/.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
46.1b
(/.f64 (+.f64 (neg.f64 b) (-.f64 (*.f64 3/2 (*.f64 (/.f64 a b) c)) b)) (*.f64 3 a))
47.6b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
43.1b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
45.6b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
32.9b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
33.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) 1/3)))
39.1b
(*.f64 -1/2 (/.f64 c b))
45.9b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
33.1b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) (*.f64 a 3))
Compiler

Compiled 5772 to 3674 computations (36.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 c (*.f64 a -3))
0.3b
(/.f64 1 (*.f64 a -3))
0.8b
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
21.7b
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))

series71.0ms (0.6%)

Counts
4 → 76
Calls

4 calls:

35.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
28.0ms
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))
6.0ms
(*.f64 c (*.f64 a -3))
1.0ms
(/.f64 1 (*.f64 a -3))

rewrite70.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
630×prod-diff_binary64
218×expm1-udef_binary64
218×log1p-udef_binary64
128×egg-rr
124×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01243
125338
2319638
Stop Event
node limit
Counts
4 → 128
Calls

4 calls:

65.0ms
(*.f64 c (*.f64 a -3))
65.0ms
(/.f64 1 (*.f64 a -3))
65.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
65.0ms
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))

simplify52.0ms (0.5%)

Algorithm
egg-herbie
Rules
455×times-frac_binary64
393×fma-neg_binary64
274×associate-/l*_binary64
267×associate-*r*_binary64
253×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0841450
12541438
28021424
344031422
Stop Event
node limit
Counts
204 → 178

prune177.0ms (1.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1762178
Fresh01111
Picked011
Done011
Total17615191
Error
5.6b
Counts
191 → 15
Alt Table
StatusErrorProgram
45.3b
(*.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (/.f64 1/3 a))
55.7b
(*.f64 (-.f64 b b) (/.f64 1/3 a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
32.9b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
46.0b
(*.f64 (-.f64 b (-.f64 (*.f64 3/2 (/.f64 a (/.f64 b c))) b)) (/.f64 1 (*.f64 a -3)))
39.1b
(*.f64 -1/2 (/.f64 c b))
33.3b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
33.4b
(/.f64 (/.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
46.1b
(/.f64 (+.f64 (neg.f64 b) (-.f64 (*.f64 3/2 (*.f64 (/.f64 a b) c)) b)) (*.f64 3 a))
47.6b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
43.1b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
45.6b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
33.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) 1/3)))
45.9b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
33.1b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) (*.f64 a 3))
Compiler

Compiled 5863 to 3994 computations (31.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) (*.f64 a 3))
0.2b
(*.f64 a (*.f64 c -3))
0.8b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b)
13.9b
(sqrt.f64 (*.f64 a (*.f64 c -3)))

series258.0ms (2.4%)

Counts
4 → 48
Calls

4 calls:

144.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) (*.f64 a 3))
94.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b)
15.0ms
(sqrt.f64 (*.f64 a (*.f64 c -3)))
4.0ms
(*.f64 a (*.f64 c -3))

rewrite183.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
937×prod-diff_binary64
458×egg-rr
141×add-sqr-sqrt_binary64
134×log1p-expm1-u_binary64
134×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01352
128552
2387652
Stop Event
node limit
Counts
4 → 458
Calls

4 calls:

166.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) (*.f64 a 3))
166.0ms
(*.f64 a (*.f64 c -3))
166.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b)
166.0ms
(sqrt.f64 (*.f64 a (*.f64 c -3)))

simplify54.0ms (0.5%)

Algorithm
egg-herbie
Rules
720×times-frac_binary64
383×associate-/l*_binary64
336×associate-/r*_binary64
278×associate-*r*_binary64
251×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061172
13281086
210721029
Stop Event
node limit
Counts
506 → 508

prune560.0ms (5.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New5035508
Fresh4812
Picked101
Done022
Total50815523
Error
3.4b
Counts
523 → 15
Alt Table
StatusErrorProgram
45.3b
(*.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (/.f64 1/3 a))
55.7b
(*.f64 (-.f64 b b) (/.f64 1/3 a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
47.7b
(/.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -3)) (sqrt.f64 a))) b) (*.f64 a 3))
32.9b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
46.0b
(*.f64 (-.f64 b (-.f64 (*.f64 3/2 (/.f64 a (/.f64 b c))) b)) (/.f64 1 (*.f64 a -3)))
33.2b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))) b)) (*.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))) b)) (/.f64 1/3 a)))
39.1b
(*.f64 -1/2 (/.f64 c b))
33.3b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
38.3b
(+.f64 (fma.f64 1 (*.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))) (/.f64 1/3 a)) (neg.f64 (*.f64 (/.f64 b 3) (/.f64 1 a)))) (fma.f64 (neg.f64 (/.f64 b 3)) (/.f64 1 a) (*.f64 (/.f64 b 3) (/.f64 1 a))))
33.4b
(/.f64 (/.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))) b) 1/3) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
46.1b
(/.f64 (+.f64 (neg.f64 b) (-.f64 (*.f64 3/2 (*.f64 (/.f64 a b) c)) b)) (*.f64 3 a))
33.1b
(pow.f64 (*.f64 3 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))) b))) -1)
45.6b
(*.f64 (/.f64 b a) -2/3)
45.6b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
Compiler

Compiled 23935 to 16163 computations (32.5% saved)

regimes5.1s (47.2%)

Accuracy

Total 7.6b remaining (74.1%)

Threshold costs 0b (0%)

Counts
214 → 3
Compiler

Compiled 22635 to 16181 computations (28.5% saved)

bsearch81.0ms (0.7%)

Steps
ItersRangePoint
9
5.211169280083627e-38
4.231882444955968e-33
7.586865080956008e-35
3
-3.4658519146892216e+158
-2.0940281063362988e+144
-1.5621525294355644e+153
Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02752
13252
Stop Event
saturated

end211.0ms (1.9%)

Compiler

Compiled 366 to 262 computations (28.4% saved)

Profiling

Loading profile data...