Details

Time bar (total: 9.2s)

analyze1.4s (15.8%)

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)

sample91.0ms (1%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
13.0ms256×body128valid
5.0ms101×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify208.0ms (2.3%)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
8.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
9.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
8.9b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
0.2b
(*.f64 (*.f64 z 9) t)
8.4b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series56.0ms (0.6%)

Counts
3 → 132
Calls

3 calls:

40.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
4.0ms
(*.f64 (*.f64 z 9) t)

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
4.0ms
(*.f64 (*.f64 z 9) t)
3.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

simplify98.0ms (1.1%)

Algorithm
egg-herbie
Rules
470×fma-def_binary64
445×*-commutative_binary64
325×div-sub_binary64
307×associate-/l*_binary64
287×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01482790
13962561
215062551
341282551
452472551

prune127.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10510115
Fresh011
Picked101
Done000
Total10611117
Error
8.6b
Counts
117 → 11
Alt Table
StatusErrorProgram
36.3b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
34.4b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
9.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
9.0b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
35.5b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
9.0b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t))) (*.f64 a 2))
9.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
43.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
33.4b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
Compiler

Compiled 2859 to 1647 computations (42.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t)))
0.2b
(*.f64 (*.f64 z 9) t)
8.4b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t))) (*.f64 a 2))

series55.0ms (0.6%)

Counts
2 → 108
Calls

2 calls:

42.0ms
(/.f64 (fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t))) (*.f64 a 2))
13.0ms
(fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 33
Calls

2 calls:

3.0ms
(/.f64 (fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t))) (*.f64 a 2))
0.0ms
(fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t)))

simplify99.0ms (1.1%)

Algorithm
egg-herbie
Rules
577×distribute-rgt-in_binary64
465×fma-def_binary64
279×div-sub_binary64
222×associate-/l*_binary64
211×associate-*l*_binary64
Counts
141 → 68
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0892397
12102009
25872009
322242009
449952009
549642009

prune93.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh01010
Picked011
Done000
Total9811109
Error
8.6b
Counts
109 → 11
Alt Table
StatusErrorProgram
36.3b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
34.4b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
9.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
9.0b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
35.5b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
9.0b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 (*.f64 z 9) t))) (*.f64 a 2))
9.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
43.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
33.4b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
Compiler

Compiled 2405 to 1494 computations (37.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 t (*.f64 z -9) (*.f64 y x))
0.3b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
8.4b
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))

series148.0ms (1.6%)

Counts
3 → 168
Calls

3 calls:

93.0ms
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))
43.0ms
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
11.0ms
(fma.f64 t (*.f64 z -9) (*.f64 y x))

rewrite59.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
230×*-un-lft-identity_binary64
230×add-sqr-sqrt_binary64
230×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
3 → 288
Calls

3 calls:

10.0ms
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
4.0ms
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))
0.0ms
(fma.f64 t (*.f64 z -9) (*.f64 y x))

simplify331.0ms (3.6%)

Algorithm
egg-herbie
Rules
419×fma-neg_binary64
404×fma-def_binary64
296×associate-/r/_binary64
234×times-frac_binary64
223×*-commutative_binary64
Counts
456 → 479
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037614401
193813425
2331713274
3474013262
4505413262

prune493.0ms (5.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4736479
Fresh459
Picked101
Done101
Total47911490
Error
8.5b
Counts
490 → 11
Alt Table
StatusErrorProgram
9.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.8b
(*.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) (sqrt.f64 2))) (/.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 2)) (cbrt.f64 a)))
9.4b
(/.f64 1 (/.f64 (*.f64 a (sqrt.f64 2)) (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2))))
9.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.4b
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 (/.f64 a (fma.f64 y x (*.f64 (*.f64 t z) -9)))))) (/.f64 1 (sqrt.f64 (*.f64 2 (/.f64 a (fma.f64 y x (*.f64 (*.f64 t z) -9)))))))
40.5b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (*.f64 y x)) (*.f64 (*.f64 t z) (*.f64 t z))) -2/81 (*.f64 -2/9 (/.f64 a (*.f64 t z)))))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
34.4b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
35.6b
(/.f64 1 (/.f64 a (/.f64 (*.f64 -9 (*.f64 t z)) 2)))
37.7b
(/.f64 1 (fma.f64 2 (/.f64 a (*.f64 y x)) (*.f64 18 (/.f64 (*.f64 a (*.f64 t z)) (*.f64 (*.f64 y x) (*.f64 y x))))))
33.4b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
Compiler

Compiled 14988 to 8894 computations (40.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
8.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series52.0ms (0.6%)

Counts
2 → 108
Calls

2 calls:

40.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify103.0ms (1.1%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune87.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New87188
Fresh01010
Picked011
Done000
Total871299
Error
8.5b
Counts
99 → 12
Alt Table
StatusErrorProgram
9.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.8b
(*.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) (sqrt.f64 2))) (/.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 2)) (cbrt.f64 a)))
9.4b
(/.f64 1 (/.f64 (*.f64 a (sqrt.f64 2)) (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2))))
9.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.4b
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 (/.f64 a (fma.f64 y x (*.f64 (*.f64 t z) -9)))))) (/.f64 1 (sqrt.f64 (*.f64 2 (/.f64 a (fma.f64 y x (*.f64 (*.f64 t z) -9)))))))
40.5b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (*.f64 y x)) (*.f64 (*.f64 t z) (*.f64 t z))) -2/81 (*.f64 -2/9 (/.f64 a (*.f64 t z)))))
33.4b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
35.6b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
34.4b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
35.6b
(/.f64 1 (/.f64 a (/.f64 (*.f64 -9 (*.f64 t z)) 2)))
37.7b
(/.f64 1 (fma.f64 2 (/.f64 a (*.f64 y x)) (*.f64 18 (/.f64 (*.f64 a (*.f64 t z)) (*.f64 (*.f64 y x) (*.f64 y x))))))
Compiler

Compiled 1969 to 1049 computations (46.7% saved)

regimes4.3s (47.2%)

Accuracy

Total 0.4b remaining (4.9%)

Threshold costs 0.4b (4.9%)

Counts
284 → 1
Compiler

Compiled 85323 to 61084 computations (28.4% saved)

simplify4.0ms (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
01522
12522
23322
33922
45022
55722
66222
76422
86322

end21.0ms (0.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 100 to 70 computations (30% saved)

sample1.2s (13.1%)

Algorithm
intervals
Results
431.0ms8000×body128valid
171.0ms3235×body128invalid
Compiler

Compiled 339 to 234 computations (31% saved)

Profiling

Loading profile data...