Details

Time bar (total: 24.3s)

analyze1.4s (5.8%)

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)

sample110.0ms (0.5%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
13.0ms256×body128valid
6.0ms115×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify214.0ms (0.9%)

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
11.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
11.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
11.4b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 z 9) t)
0.5b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
10.8b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series61.0ms (0.3%)

Counts
3 → 132
Calls

3 calls:

46.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
10.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
4.0ms
(*.f64 (*.f64 z 9) t)

rewrite34.0ms (0.1%)

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:

24.0ms
(/.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))

simplify91.0ms (0.4%)

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

prune124.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New10510115
Fresh011
Picked011
Done000
Total10512117
Error
11.0b
Counts
117 → 12
Alt Table
StatusErrorProgram
43.1b
(/.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))))))
36.5b
(/.f64 (*.f64 y x) (*.f64 a 2))
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))
12.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
34.2b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
37.7b
(/.f64 (/.f64 (fma.f64 t (*.f64 t (*.f64 (*.f64 z z) -81)) (*.f64 (*.f64 y x) (*.f64 y x))) (fma.f64 t (*.f64 z 9) (*.f64 y x))) (*.f64 a 2))
34.7b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
11.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
11.4b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.2b
(/.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)))
11.7b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
34.2b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
Compiler

Compiled 2883 to 1656 computations (42.6% saved)

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.6b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
10.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series60.0ms (0.2%)

Counts
2 → 108
Calls

2 calls:

49.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
11.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite10.0ms (0%)

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:

7.0ms
(*.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))

simplify107.0ms (0.4%)

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

prune104.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New85388
Fresh3710
Picked101
Done101
Total9010100
Error
11.0b
Counts
100 → 10
Alt Table
StatusErrorProgram
36.5b
(/.f64 (*.f64 y x) (*.f64 a 2))
12.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
11.7b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
34.2b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
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))
12.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
34.2b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
37.7b
(/.f64 (/.f64 (fma.f64 t (*.f64 t (*.f64 (*.f64 z z) -81)) (*.f64 (*.f64 y x) (*.f64 y x))) (fma.f64 t (*.f64 z 9) (*.f64 y x))) (*.f64 a 2))
34.7b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
11.8b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 2150 to 1166 computations (45.8% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.4b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
0.6b
(fma.f64 t (*.f64 z -9) (*.f64 y x))
10.8b
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))

series149.0ms (0.6%)

Counts
3 → 168
Calls

3 calls:

100.0ms
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))
39.0ms
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
10.0ms
(fma.f64 t (*.f64 z -9) (*.f64 y x))

rewrite57.0ms (0.2%)

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))

simplify334.0ms (1.4%)

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

prune491.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New4727479
Fresh459
Picked101
Done000
Total47712489
Error
11.0b
Counts
489 → 12
Alt Table
StatusErrorProgram
36.3b
(/.f64 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
34.4b
(/.f64 1 (*.f64 -2/9 (/.f64 a (*.f64 t z))))
34.2b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
40.4b
(/.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))))))
36.5b
(/.f64 (*.f64 y x) (*.f64 a 2))
12.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
11.7b
(/.f64 (/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (/.f64 a (/.f64 1 2)))
12.8b
(*.f64 (/.f64 1 (/.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))))) (/.f64 1 (/.f64 (cbrt.f64 a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 2)))))
34.2b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
39.7b
(/.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)))))
12.0b
(/.f64 1 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2)))))
11.8b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 15012 to 8924 computations (40.6% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x))))
0.6b
(fma.f64 t (*.f64 z -9) (*.f64 y x))
0.8b
(/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))
10.8b
(/.f64 (/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (/.f64 a (/.f64 1 2)))

series95.0ms (0.4%)

Counts
3 → 156
Calls

3 calls:

42.0ms
(/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))
42.0ms
(/.f64 (/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (/.f64 a (/.f64 1 2)))
10.0ms
(/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x))))

rewrite729.0ms (3%)

Algorithm
rewrite-expression-head
Rules
7960×times-frac_binary64
3203×*-un-lft-identity_binary64
3203×add-sqr-sqrt_binary64
3203×add-cube-cbrt_binary64
367×div-inv_binary64
Counts
3 → 2232
Calls

3 calls:

44.0ms
(/.f64 (/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (/.f64 a (/.f64 1 2)))
7.0ms
(/.f64 1 (/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x))))
2.0ms
(/.f64 1 (fma.f64 t (*.f64 z -9) (*.f64 y x)))

simplify2.3s (9.4%)

Algorithm
egg-herbie
Rules
510×associate-*l/_binary64
464×associate-/l/_binary64
424×associate-/r/_binary64
406×*-commutative_binary64
368×associate-/r*_binary64
Counts
2388 → 2153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
055695787
1132793576
2481493528
3507893528

prune3.0s (12.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New217332176
Fresh11011
Picked101
Done000
Total2175132188
Error
11.0b
Counts
2188 → 13
Alt Table
StatusErrorProgram
36.3b
(/.f64 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
34.4b
(/.f64 1 (*.f64 -2/9 (/.f64 a (*.f64 t z))))
34.2b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
40.4b
(/.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))))))
12.8b
(*.f64 (/.f64 1 (/.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))))) (/.f64 1 (/.f64 (cbrt.f64 a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 2)))))
34.2b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
39.7b
(/.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)))))
36.5b
(/.f64 (/.f64 1 (/.f64 1 (*.f64 y x))) (/.f64 a (/.f64 1 2)))
12.0b
(/.f64 1 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2)))))
34.4b
(/.f64 (/.f64 1 (/.f64 1 (*.f64 (*.f64 t z) -9))) (/.f64 a (/.f64 1 2)))
11.8b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
36.5b
(/.f64 (*.f64 y x) (*.f64 a 2))
11.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2)) (/.f64 a (/.f64 1 (sqrt.f64 2))))
Compiler

Compiled 94911 to 67132 computations (29.3% saved)

regimes13.6s (55.8%)

Accuracy

Total 0.5b remaining (6.8%)

Threshold costs 0.5b (6.8%)

Counts
761 → 1
Compiler

Compiled 287133 to 223157 computations (22.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
unpow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01717
12117
21917

end20.0ms (0.1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 85 to 60 computations (29.4% saved)

sample1.2s (5%)

Algorithm
intervals
Results
425.0ms8000×body128valid
166.0ms3099×body128invalid
Compiler

Compiled 344 to 249 computations (27.6% saved)

Profiling

Loading profile data...