Details

Time bar (total: 12.0s)

analyze1.7s (13.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.6s (13.3%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
441.0ms3249×body128invalid
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify210.0ms (1.7%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune6.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
7.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series50.0ms (0.4%)

Counts
2 → 108
Calls

2 calls:

35.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
15.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite65.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
633×log-prod_binary64
240×expm1-udef_binary64
240×log1p-udef_binary64
212×log-pow_binary64
170×prod-diff_binary64
Counts
2 → 60
Calls

2 calls:

63.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
63.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01328
126728
2309128
3552428
000
100

simplify162.0ms (1.3%)

Algorithm
egg-herbie
Rules
1901×fma-def_binary64
641×fma-neg_binary64
512×cancel-sign-sub-inv_binary64
426×associate-/l*_binary64
420×distribute-rgt-neg-in_binary64
Counts
168 → 73
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0321566
1881398
22131398
35451398
411591398
521651398
628561398
734151398
834091398
934981398
1035341398
1151621398

prune86.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New611273
Fresh011
Picked101
Done000
Total621375
Error
7.6b
Counts
75 → 13
Alt Table
StatusErrorProgram
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.8b
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) 3) (/.f64 1/2 a))
31.6b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
39.8b
(cbrt.f64 (pow.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)) 3))
31.2b
(pow.f64 (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) 2)
8.8b
(pow.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) 3)
35.9b
(/.f64 (/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) (sqrt.f64 a)) (sqrt.f64 a))
28.3b
(/.f64 (/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) (cbrt.f64 (*.f64 a a))) (cbrt.f64 a))
8.1b
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
33.7b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
8.0b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
33.7b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
7.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
Compiler

Compiled 1669 to 958 computations (42.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
0.2b
(*.f64 9/2 (/.f64 (*.f64 t z) a))
5.1b
(/.f64 (*.f64 y x) a)
7.2b
(/.f64 (*.f64 t z) a)

series75.0ms (0.6%)

Counts
4 → 24
Calls

4 calls:

34.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
16.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
12.0ms
(/.f64 (*.f64 y x) a)
12.0ms
(/.f64 (*.f64 t z) a)

rewrite93.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
305×log1p-udef_binary64
170×add-sqr-sqrt_binary64
162×egg-rr
160×log1p-expm1-u_binary64
160×expm1-log1p-u_binary64
Counts
4 → 162
Calls

4 calls:

90.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
90.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
90.0ms
(/.f64 (*.f64 y x) a)
90.0ms
(/.f64 (*.f64 t z) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01546
133543
2455243
3497543
000
100

simplify163.0ms (1.4%)

Algorithm
egg-herbie
Rules
1536×fma-neg_binary64
454×associate-/l*_binary64
309×div-sub_binary64
270×fma-def_binary64
250×associate-/r/_binary64
Counts
186 → 167
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023348
159324
2147324
3368324
4764324
51405324
61667324
71970324
82253324
92415324
102451324
112470324
122485324
132404324
142392324
152392324
162231324

prune195.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1607167
Fresh8412
Picked101
Done000
Total16911180
Error
0.7b
Counts
180 → 11
Alt Table
StatusErrorProgram
8.5b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y 1) (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.8b
(pow.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) 3)
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.8b
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) 3) (/.f64 1/2 a))
21.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (cbrt.f64 (*.f64 a a))) (/.f64 z (cbrt.f64 a)))))
8.1b
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
9.9b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y a) x)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (*.f64 z (/.f64 1 a)))))
8.7b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (/.f64 1 (/.f64 a z)))))
7.9b
(/.f64 (-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2)) a)
8.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (/.f64 (*.f64 t 9/2) (/.f64 a z)))
Compiler

Compiled 4217 to 1948 computations (53.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (*.f64 y x) 1/2)
0.2b
(*.f64 (*.f64 t z) 9/2)
0.2b
(-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2))
7.5b
(/.f64 (-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2)) a)

series59.0ms (0.5%)

Counts
4 → 156
Calls

4 calls:

37.0ms
(/.f64 (-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2)) a)
12.0ms
(-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2))
6.0ms
(*.f64 (*.f64 t z) 9/2)
4.0ms
(*.f64 (*.f64 y x) 1/2)

rewrite96.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
283×expm1-udef_binary64
283×log1p-udef_binary64
258×fma-neg_binary64
160×egg-rr
158×add-sqr-sqrt_binary64
Counts
4 → 160
Calls

4 calls:

91.0ms
(*.f64 (*.f64 y x) 1/2)
91.0ms
(*.f64 (*.f64 t z) 9/2)
91.0ms
(-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2))
91.0ms
(/.f64 (-.f64 (*.f64 (*.f64 y x) 1/2) (*.f64 (*.f64 t z) 9/2)) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01449
131045
2406845
3510045
000
100

simplify294.0ms (2.4%)

Algorithm
egg-herbie
Rules
1470×fma-neg_binary64
456×associate-/l*_binary64
307×div-sub_binary64
298×fma-def_binary64
245×distribute-rgt-neg-in_binary64
Counts
316 → 172
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0262028
1681860
21611860
34031860
48031860
514111860
616671860
719761860
822551860
924151860
1024511860
1124701860
1224851860
1324041860
1423921860
1523921860
1622311860

prune231.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1711172
Fresh1910
Picked101
Done000
Total17310183
Error
0.7b
Counts
183 → 10
Alt Table
StatusErrorProgram
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.8b
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) 3) (/.f64 1/2 a))
21.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (cbrt.f64 (*.f64 a a))) (/.f64 z (cbrt.f64 a)))))
8.4b
(/.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 y x) 1/2)) 3) (*.f64 (*.f64 t z) 9/2)) a)
8.1b
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
9.9b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y a) x)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y 1) (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (*.f64 z (/.f64 1 a)))))
8.7b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (/.f64 1 (/.f64 a z)))))
8.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (/.f64 (*.f64 t 9/2) (/.f64 a z)))
Compiler

Compiled 4049 to 2218 computations (45.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
0.3b
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
7.5b
(/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2))

series254.0ms (2.1%)

Counts
2 → 120
Calls

2 calls:

216.0ms
(/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2))
37.0ms
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))

rewrite138.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
267×expm1-udef_binary64
267×log1p-udef_binary64
210×fma-neg_binary64
188×prod-diff_binary64
173×fma-udef_binary64
Counts
2 → 89
Calls

2 calls:

134.0ms
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
134.0ms
(/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01537
130734
2362134
3496234
4499634
5500534
000
100

simplify86.0ms (0.7%)

Algorithm
egg-herbie
Rules
691×associate-*l*_binary64
493×associate-*r/_binary64
474×associate-*l/_binary64
376×fma-def_binary64
248×associate-/r/_binary64
Counts
209 → 118
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01233576
14463456
216463432
354833432

prune160.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1520152
Fresh099
Picked011
Done000
Total15210162
Error
0.7b
Counts
162 → 10
Alt Table
StatusErrorProgram
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.8b
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) 3) (/.f64 1/2 a))
21.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (cbrt.f64 (*.f64 a a))) (/.f64 z (cbrt.f64 a)))))
8.4b
(/.f64 (-.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 y x) 1/2)) 3) (*.f64 (*.f64 t z) 9/2)) a)
8.1b
(/.f64 1 (/.f64 a (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)))
9.9b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y a) x)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y 1) (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (*.f64 z (/.f64 1 a)))))
8.7b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (/.f64 1 (/.f64 a z)))))
8.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (/.f64 (*.f64 t 9/2) (/.f64 a z)))
Compiler

Compiled 3526 to 1928 computations (45.3% saved)

regimes5.2s (43.4%)

Accuracy

Total 6.1b remaining (93.1%)

Threshold costs 0b (0%)

Counts
104 → 7
Compiler

Compiled 22925 to 16808 computations (26.7% saved)

bsearch10.0ms (0.1%)

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Rules
23×*-commutative_binary64
13×+-commutative_binary64
13×sub-neg_binary64
10×distribute-lft-neg-in_binary64
10×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055203
181203
299203
3124203
4146203
5157203
6161203
7159203

end1.1s (8.8%)

Compiler

Compiled 1068 to 638 computations (40.3% saved)

Profiling

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