Details

Time bar (total: 8.7s)

analyze618.0ms (7.1%)

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)

sample2.2s (25.2%)

Results
687.0ms5359×body128valid
595.0ms1160×body2048valid
321.0ms776×body1024valid
247.0ms413×body4096valid
133.0ms1058×body128invalid
107.0ms360×body512valid
39.0ms188×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify33.0ms (0.4%)

Algorithm
egg-herbie
Rules
763×fma-neg_binary64
619×times-frac_binary64
367×fma-def_binary64
242×distribute-rgt-in_binary64
239×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
27222
316322
426722
543622
674722
7133522
8268922
9408622
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
30.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
30.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
30.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
1.0b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
1.8b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
20.2b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series118.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

51.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
32.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
26.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
9.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite74.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
278×log1p-udef_binary64
166×add-sqr-sqrt_binary64
162×log1p-expm1-u_binary64
162×expm1-log1p-u_binary64
161×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01574
134262
2486562
Stop Event
node limit
Counts
4 → 158
Calls

4 calls:

71.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
71.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
71.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
71.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

simplify46.0ms (0.5%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
432×fma-def_binary64
422×associate-/r*_binary64
142×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
14022164
214032078
Stop Event
node limit
Counts
254 → 232

prune212.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22210232
Fresh011
Picked101
Done000
Total22311234
Error
5.3b
Counts
234 → 11
Alt Table
StatusErrorProgram
46.8b
(pow.f64 (cbrt.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))) (/.f64 1/2 a))) 3)
46.1b
(/.f64 (*.f64 (/.f64 -2 b) (*.f64 c a)) (*.f64 2 a))
32.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 2)))) (*.f64 2 a))
46.1b
(/.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (*.f64 2 a))
44.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (*.f64 2 a))
43.2b
(-.f64 (/.f64 c b) (/.f64 b a))
41.1b
(/.f64 (neg.f64 c) b)
46.7b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (/.f64 1/2 a)))
30.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
42.9b
(/.f64 (neg.f64 b) a)
55.1b
(exp.f64 (log.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))) (/.f64 1/2 a))))
Compiler

Compiled 6208 to 3877 computations (37.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
1.2b
(fma.f64 b b (*.f64 a (*.f64 c -4)))
1.8b
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
20.2b
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))

series114.0ms (1.3%)

Counts
4 → 96
Calls

4 calls:

48.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
31.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
26.0ms
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))
8.0ms
(fma.f64 b b (*.f64 a (*.f64 c -4)))

rewrite72.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
737×prod-diff_binary64
158×egg-rr
139×add-sqr-sqrt_binary64
132×log1p-expm1-u_binary64
132×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01362
128159
2362659
Stop Event
node limit
Counts
4 → 158
Calls

4 calls:

67.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
67.0ms
(fma.f64 b b (*.f64 a (*.f64 c -4)))
67.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
67.0ms
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))

simplify45.0ms (0.5%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
432×fma-def_binary64
422×associate-/r*_binary64
142×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
14022164
214032078
Stop Event
node limit
Counts
254 → 232

prune213.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2266232
Fresh4610
Picked011
Done000
Total23013243
Error
5.3b
Counts
243 → 13
Alt Table
StatusErrorProgram
43.4b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
41.1b
(/.f64 (neg.f64 c) b)
46.1b
(/.f64 (*.f64 (/.f64 -2 b) (*.f64 c a)) (*.f64 2 a))
32.6b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
43.0b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (*.f64 2 a))
43.2b
(-.f64 (/.f64 c b) (/.f64 b a))
32.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
46.1b
(/.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (*.f64 2 a))
30.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
32.9b
(*.f64 (fma.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (neg.f64 b)) (/.f64 1/2 a))
42.9b
(/.f64 (neg.f64 b) a)
46.1b
(exp.f64 (log.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
Compiler

Compiled 5978 to 3733 computations (37.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2))
0.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
0.7b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
14.3b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series450.0ms (5.2%)

Counts
4 → 36
Calls

4 calls:

228.0ms
(/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2))
130.0ms
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
79.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
12.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

rewrite86.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
593×prod-diff_binary64
165×egg-rr
158×add-sqr-sqrt_binary64
149×add-cbrt-cube_binary64
149×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01569
132466
2421866
Stop Event
node limit
Counts
4 → 165
Calls

4 calls:

82.0ms
(/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2))
82.0ms
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
82.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
82.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

simplify37.0ms (0.4%)

Algorithm
egg-herbie
Rules
585×associate-/l*_binary64
560×associate-/r*_binary64
397×fma-def_binary64
218×cancel-sign-sub-inv_binary64
212×associate-*r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01381518
14501376
215091333
Stop Event
node limit
Counts
201 → 237

prune265.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2352237
Fresh4711
Picked011
Done011
Total23911250
Error
3.6b
Counts
250 → 11
Alt Table
StatusErrorProgram
43.4b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
41.1b
(/.f64 (neg.f64 c) b)
46.2b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) 1/2)))
32.6b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
43.0b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (*.f64 2 a))
43.2b
(-.f64 (/.f64 c b) (/.f64 b a))
32.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
30.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
32.9b
(*.f64 (fma.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (neg.f64 b)) (/.f64 1/2 a))
44.8b
(/.f64 1 (fma.f64 4 (/.f64 a (/.f64 c (/.f64 b (*.f64 a -4)))) (/.f64 a b)))
Compiler

Compiled 6299 to 4270 computations (32.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a)))
0.4b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
0.7b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
14.3b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series1.2s (13.9%)

Counts
2 → 24
Calls

2 calls:

798.0ms
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
412.0ms
(cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a)))

rewrite67.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
575×prod-diff_binary64
158×add-sqr-sqrt_binary64
153×log1p-expm1-u_binary64
153×expm1-log1p-u_binary64
151×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01644
134544
2413244
Stop Event
node limit
Counts
2 → 92
Calls

2 calls:

65.0ms
(cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a)))
65.0ms
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)

simplify49.0ms (0.6%)

Algorithm
egg-herbie
Rules
825×associate-/l*_binary64
776×associate-/r*_binary64
412×fma-def_binary64
238×associate-/r/_binary64
156×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01712203
15281964
218571890
Stop Event
node limit
Counts
116 → 140

prune196.0ms (2.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New2382240
Fresh088
Picked011
Done022
Total23813251
Error
3.6b
Counts
251 → 13
Alt Table
StatusErrorProgram
43.4b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
41.1b
(/.f64 (neg.f64 c) b)
46.2b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) 1/2)))
32.6b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
43.0b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))))) (*.f64 2 a))
43.2b
(-.f64 (/.f64 c b) (/.f64 b a))
32.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
43.4b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 b -2) (/.f64 1/2 a))) 3)
46.5b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
30.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
32.9b
(*.f64 (fma.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 1/4) (neg.f64 b)) (/.f64 1/2 a))
44.8b
(/.f64 1 (fma.f64 4 (/.f64 a (/.f64 c (/.f64 b (*.f64 a -4)))) (/.f64 a b)))
Compiler

Compiled 7931 to 5624 computations (29.1% saved)

regimes2.3s (26.5%)

Accuracy

Total 7.2b remaining (71.3%)

Threshold costs 0b (0%)

Counts
222 → 3
Compiler

Compiled 19052 to 13546 computations (28.9% saved)

bsearch57.0ms (0.7%)

Steps
ItersRangePoint
6
2.384241652144152e-61
3.043608990902108e-60
3.181936558569041e-61
6
-4.7081372626711444e+120
-4.3432842671613634e+119
-4.637978985458623e+120
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
02651
14149
25049
35649
45849
Stop Event
saturated

end177.0ms (2%)

Compiler

Compiled 306 to 213 computations (30.4% saved)

Profiling

Loading profile data...