Details

Time bar (total: 20.0s)

analyze1.8s (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
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample86.0ms (0.4%)

Algorithm
intervals
Results
20.0ms35×body2048valid
18.0ms162×body128valid
15.0ms35×body1024valid
7.0ms10×body4096valid
3.0msbody512valid
3.0ms26×body128nan
1.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify103.0ms (0.5%)

Algorithm
egg-herbie
Rules
518×div-sub_binary64
428×fma-neg_binary64
246×associate-/l*_binary64
205×fma-def_binary64
183×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
12720
25420
311520
417920
529120
641720
752820
860220
985420
10180220
11104320
12102720
13103520
14104320
15104320
16110120
17113720
18113920
19115120
20104620

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
34.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
34.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 48 to 30 computations (37.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
0.7b
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
1.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
21.5b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series432.0ms (2.2%)

Counts
4 → 96
Calls

4 calls:

177.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
156.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
81.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
17.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite112.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt_binary64
80×*-un-lft-identity_binary64
61×prod-diff_binary64
60×add-cube-cbrt_binary64
41×sqrt-prod_binary64
Counts
4 → 176
Calls

4 calls:

35.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
22.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
6.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
5.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify551.0ms (2.8%)

Algorithm
egg-herbie
Rules
819×fma-neg_binary64
295×cancel-sign-sub-inv_binary64
181×unswap-sqr_binary64
169×sub-neg_binary64
135×associate-*r*_binary64
Counts
272 → 292
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03177693
17796304
226825750
345845750
449745750

prune453.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2857292
Fresh000
Picked011
Done000
Total2858293
Error
3.6b
Counts
293 → 8
Alt Table
StatusErrorProgram
32.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
33.1b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
42.9b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
38.9b
(*.f64 -1/2 (/.f64 c b_2))
45.5b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
32.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
34.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
45.7b
(/.f64 (*.f64 -2 b_2) a)
Compiler

Compiled 8994 to 1942 computations (78.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
0.1b
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
0.1b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
8.6b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.6s (7.8%)

Counts
4 → 42
Calls

4 calls:

775.0ms
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
437.0ms
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
322.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
32.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite104.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
172×*-un-lft-identity_binary64
162×times-frac_binary64
139×add-sqr-sqrt_binary64
104×add-cube-cbrt_binary64
34×distribute-lft-out--_binary64
Counts
4 → 244
Calls

4 calls:

18.0ms
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
12.0ms
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
10.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
3.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify466.0ms (2.3%)

Algorithm
egg-herbie
Rules
715×fma-def_binary64
401×fma-neg_binary64
292×cancel-sign-sub-inv_binary64
186×sub-neg_binary64
153×distribute-frac-neg_binary64
Counts
286 → 378
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03499160
17948172
227057612
347987608
449067608

prune401.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3753378
Fresh246
Picked011
Done011
Total3779386
Error
0.0b
Counts
386 → 9
Alt Table
StatusErrorProgram
32.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
46.1b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
48.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
33.1b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
38.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.9b
(*.f64 -1/2 (/.f64 c b_2))
45.5b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
32.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
34.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 11597 to 2905 computations (75% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
0.2b
(*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
0.2b
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))
8.6b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series5.4s (27.1%)

Counts
3 → 42
Calls

3 calls:

3.5s
(*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
1.4s
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))
465.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))

rewrite195.0ms (1%)

Algorithm
rewrite-expression-head
Rules
212×*-un-lft-identity_binary64
182×cbrt-prod_binary64
151×times-frac_binary64
144×add-sqr-sqrt_binary64
80×add-cube-cbrt_binary64
Counts
3 → 223
Calls

3 calls:

44.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
40.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
8.0ms
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))

simplify582.0ms (2.9%)

Algorithm
egg-herbie
Rules
645×fma-def_binary64
383×associate-*r*_binary64
345×associate-*l*_binary64
226×*-commutative_binary64
226×fma-neg_binary64
Counts
265 → 314
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044614247
1108113593
2367012261
3497712261
4495212261

prune567.0ms (2.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5141515
Fresh156
Picked011
Done022
Total5159524
Error
0.0b
Counts
524 → 9
Alt Table
StatusErrorProgram
32.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
46.1b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
32.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
45.4b
(*.f64 (/.f64 b_2 a) -2)
48.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
33.1b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
38.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.9b
(*.f64 -1/2 (/.f64 c b_2))
34.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 29041 to 5734 computations (80.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
1.4b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
5.2b
(/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
8.6b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.6s (8.1%)

Counts
3 → 36
Calls

3 calls:

968.0ms
(/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
483.0ms
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
161.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

rewrite28.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
58×times-frac_binary64
47×*-un-lft-identity_binary64
47×add-sqr-sqrt_binary64
33×add-cube-cbrt_binary64
17×add-cbrt-cube_binary64
Counts
3 → 125
Calls

3 calls:

7.0ms
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
5.0ms
(/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

simplify183.0ms (0.9%)

Algorithm
egg-herbie
Rules
720×fma-def_binary64
390×cancel-sign-sub-inv_binary64
251×fma-neg_binary64
247×times-frac_binary64
196×associate-/l*_binary64
Counts
161 → 236
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03315674
18724918
232664799
348074797
449664797
549094797

prune144.0ms (0.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New2630263
Fresh055
Picked011
Done033
Total2639272
Error
0.0b
Counts
272 → 9
Alt Table
StatusErrorProgram
32.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
46.1b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
32.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
45.4b
(*.f64 (/.f64 b_2 a) -2)
48.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
33.1b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
38.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.9b
(*.f64 -1/2 (/.f64 c b_2))
34.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 7596 to 1785 computations (76.5% saved)

regimes3.4s (17.1%)

Accuracy

Total 8.3b remaining (98.5%)

Threshold costs 0b (0%)

Counts
202 → 4
Compiler

Compiled 22647 to 11725 computations (48.2% saved)

bsearch74.0ms (0.4%)

Steps
ItersRangePoint
5
8.931405685114294e+88
2.746859577346239e+89
1.2798399534946243e+89
8
1.015675176524763e-200
1.631477822442049e-196
3.470829932155455e-200
6
-30286195606073.355
-6970773915111.175
-22357588223804.316
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03776
15776
27276
38676
49376
59676
69776
79676

end1.0ms (0%)

Compiler

Compiled 54 to 32 computations (40.7% saved)

sample1.6s (7.9%)

Algorithm
intervals
Results
392.0ms1115×body2048valid
305.0ms5231×body128valid
177.0ms766×body1024valid
121.0ms375×body4096valid
58.0ms352×body512valid
44.0ms792×body128nan
17.0ms161×body256valid
15.0ms277×body128invalid
Compiler

Compiled 238 to 142 computations (40.3% saved)

Profiling

Loading profile data...