Details

Time bar (total: 12.1s)

analyze666.0ms (5.5%)

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)

sample2.3s (19.3%)

Results
737.0ms5372×body128valid
655.0ms1201×body2048valid
327.0ms740×body1024valid
243.0ms375×body4096valid
140.0ms1077×body128invalid
125.0ms373×body512valid
46.0ms195×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify30.0ms (0.3%)

Algorithm
egg-herbie
Rules
747×fma-neg_binary64
619×times-frac_binary64
338×fma-def_binary64
314×associate-/l*_binary64
262×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13422
26922
316122
425922
541722
673422
7132622
8261822
9387722
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
35.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
35.7b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
35.8b
(*.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)

localize11.0ms (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 4 (*.f64 a c))))) (*.f64 2 a))
0.3b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series123.0ms (1%)

Counts
4 → 96
Calls

4 calls:

54.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
32.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
26.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
11.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

rewrite71.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
277×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
134362
2485962
Stop Event
node limit
Counts
4 → 158
Calls

4 calls:

67.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
67.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
67.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
67.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

simplify48.0ms (0.4%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
430×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

prune187.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2257232
Fresh011
Picked101
Done000
Total2268234
Error
4.6b
Counts
234 → 8
Alt Table
StatusErrorProgram
44.4b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 2 a))
45.4b
(-.f64 (/.f64 c b) (/.f64 b a))
45.2b
(/.f64 (neg.f64 b) a)
38.5b
(/.f64 (neg.f64 c) b)
55.8b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
47.0b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a))
46.9b
(*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2))
35.8b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
Compiler

Compiled 6096 to 3532 computations (42.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
0.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
0.5b
(fma.f64 b b (*.f64 a (*.f64 c -4)))
24.4b
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))

series120.0ms (1%)

Counts
4 → 96
Calls

4 calls:

50.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
33.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
27.0ms
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))
9.0ms
(fma.f64 b b (*.f64 a (*.f64 c -4)))

rewrite71.0ms (0.6%)

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

simplify48.0ms (0.4%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
466×associate-/l*_binary64
432×fma-def_binary64
423×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

prune171.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2284232
Fresh257
Picked011
Done000
Total23010240
Error
4.6b
Counts
240 → 10
Alt Table
StatusErrorProgram
37.1b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
50.8b
(/.f64 (-.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 3/2) (pow.f64 b 3)) (*.f64 (*.f64 a 2) (+.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
35.8b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
45.3b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.4b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 2 a))
45.4b
(-.f64 (/.f64 c b) (/.f64 b a))
55.8b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
38.5b
(/.f64 (neg.f64 c) b)
47.0b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a))
46.9b
(*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2))
Compiler

Compiled 5976 to 3711 computations (37.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
0.2b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
2.4b
(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)))
11.8b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series320.0ms (2.6%)

Counts
4 → 36
Calls

4 calls:

133.0ms
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
87.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)))
85.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
15.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

rewrite75.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
575×prod-diff_binary64
174×egg-rr
148×add-sqr-sqrt_binary64
141×log1p-expm1-u_binary64
141×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01560
130660
2382660
Stop Event
node limit
Counts
4 → 174
Calls

4 calls:

71.0ms
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
71.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
71.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)))
71.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

simplify35.0ms (0.3%)

Algorithm
egg-herbie
Rules
728×times-frac_binary64
385×associate-/l*_binary64
360×associate-/r*_binary64
271×associate-*r*_binary64
249×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01021433
13231314
210541236
Stop Event
node limit
Counts
210 → 169

prune145.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1672169
Fresh178
Picked101
Done011
Total16910179
Error
2.7b
Counts
179 → 10
Alt Table
StatusErrorProgram
38.2b
(*.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b)))) (/.f64 1/2 a))
47.8b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) (/.f64 1/2 a))
44.4b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 2 a))
45.4b
(-.f64 (/.f64 c b) (/.f64 b a))
55.8b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
38.5b
(/.f64 (neg.f64 c) b)
50.8b
(/.f64 (-.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 3/2) (pow.f64 b 3)) (*.f64 (*.f64 a 2) (+.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
47.0b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a))
46.9b
(*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2))
35.8b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
Compiler

Compiled 4707 to 3031 computations (35.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b)))
1.3b
(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2))
2.5b
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))))
11.8b
(sqrt.f64 (*.f64 c (*.f64 -4 a)))

series3.3s (27.1%)

Counts
4 → 36
Calls

4 calls:

1.8s
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))))
977.0ms
(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2))
484.0ms
(cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b)))
13.0ms
(sqrt.f64 (*.f64 c (*.f64 -4 a)))

rewrite63.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
587×prod-diff_binary64
151×add-sqr-sqrt_binary64
144×log1p-expm1-u_binary64
144×expm1-log1p-u_binary64
143×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01667
133667
2376767
Stop Event
node limit
Counts
4 → 120
Calls

4 calls:

61.0ms
(cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b)))
61.0ms
(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2))
61.0ms
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b))))
61.0ms
(sqrt.f64 (*.f64 c (*.f64 -4 a)))

simplify88.0ms (0.7%)

Algorithm
egg-herbie
Rules
515×times-frac_binary64
440×fma-def_binary64
380×associate-/l*_binary64
336×associate-/r*_binary64
315×associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04658124
116926795
Stop Event
node limit
Counts
156 → 190

prune402.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2631264
Fresh088
Picked101
Done011
Total26410274
Error
2.7b
Counts
274 → 10
Alt Table
StatusErrorProgram
46.9b
(*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2))
52.0b
(*.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 -4 a)) (sqrt.f64 c))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 -4 a)))) b)))) (/.f64 1/2 a))
44.4b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 2 a))
47.8b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) (/.f64 1/2 a))
45.4b
(-.f64 (/.f64 c b) (/.f64 b a))
55.8b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
38.5b
(/.f64 (neg.f64 c) b)
50.8b
(/.f64 (-.f64 (pow.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) 3/2) (pow.f64 b 3)) (*.f64 (*.f64 a 2) (+.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))
47.0b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) 2) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) a))
35.8b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
Compiler

Compiled 19136 to 14514 computations (24.2% saved)

regimes3.6s (29.4%)

Accuracy

Total 8.1b remaining (72.9%)

Threshold costs 0b (0%)

Counts
220 → 3
Compiler

Compiled 20344 to 14194 computations (30.2% saved)

bsearch58.0ms (0.5%)

Steps
ItersRangePoint
7
3.8806250349188764e-196
8.597166853144995e-195
8.478314556974444e-195
6
-2.996560351873491e+130
-4.000158892863278e+129
-1.4230140549006078e+130
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: 0 (0.0ms)

IterNodesCost
02651
13551
24451
35151
45551
55651
Stop Event
saturated

end161.0ms (1.3%)

Compiler

Compiled 317 to 208 computations (34.4% saved)

Profiling

Loading profile data...