Details

Time bar (total: 10.9s)

analyze995.0ms (9.2%)

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
6.2%93.6%0.2%9
6.2%82.7%11.1%10
12.5%73.7%13.8%11
15.6%59.5%25%12
17.9%53.3%28.8%13
22.4%47.2%30.4%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.7s (15.6%)

Results
1.1s8256×body128valid
406.0ms3126×body128invalid
Compiler

Compiled 53 to 35 computations (34% saved)

simplify66.0ms (0.6%)

Algorithm
egg-herbie
Rules
853×fma-neg_binary64
525×fma-def_binary64
182×cancel-sign-sub-inv_binary64
160×associate-*l*_binary64
154×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
12517
27217
322717
451217
5104417
6143617
7149217
8157317
9161517
10163117
11163117
12155017

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
4.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
4.6b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
4.3b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series35.0ms (0.3%)

Counts
1 → 48
Calls

1 calls:

35.0ms
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

5.0ms
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

simplify105.0ms (1%)

Algorithm
egg-herbie
Rules
656×associate-*l*_binary64
618×exp-prod_binary64
546×associate-*r*_binary64
433×distribute-rgt-in_binary64
424×distribute-lft-in_binary64
Counts
58 → 33
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0421181
1101928
2231928
3721928
43522928
54742928
64963928
74910928

prune29.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New28533
Fresh000
Picked011
Done000
Total28634
Error
4.0b
Counts
34 → 6
Alt Table
StatusErrorProgram
25.9b
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
43.7b
(cbrt.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
4.6b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
37.2b
(*.f64 4 (*.f64 y t))
28.2b
(fma.f64 x x (*.f64 (*.f64 y (*.f64 z z)) -4))
40.6b
(pow.f64 x 2)
Compiler

Compiled 722 to 316 computations (56.2% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
2.0b
(sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
4.3b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series226.0ms (2.1%)

Counts
2 → 80
Calls

2 calls:

191.0ms
(sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
35.0ms
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 68
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
1.0ms
(sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))

simplify112.0ms (1%)

Algorithm
egg-herbie
Rules
617×cancel-sign-sub-inv_binary64
264×fma-neg_binary64
249×sub-neg_binary64
201×associate-*r*_binary64
187×unswap-sqr_binary64
Counts
148 → 147
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02545290
17844698
233384601
350584601

prune319.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2804284
Fresh134
Picked101
Done011
Total2828290
Error
4.0b
Counts
290 → 8
Alt Table
StatusErrorProgram
26.5b
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
26.1b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
26.6b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))) (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
43.7b
(cbrt.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
4.6b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
37.2b
(*.f64 4 (*.f64 y t))
26.3b
(*.f64 (*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
40.6b
(pow.f64 x 2)
Compiler

Compiled 13634 to 6889 computations (49.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
2.0b
(sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
4.3b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series808.0ms (7.4%)

Counts
2 → 96
Calls

2 calls:

771.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
37.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
51×sqrt-pow1_binary64
48×pow1_binary64
42×add-sqr-sqrt_binary64
37×sqrt-prod_binary64
36×pow-prod-up_binary64
Counts
2 → 100
Calls

2 calls:

12.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
6.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

simplify329.0ms (3%)

Algorithm
egg-herbie
Rules
501×*-commutative_binary64
242×associate-*r*_binary64
237×+-commutative_binary64
214×fma-def_binary64
186×associate-+r+_binary64
Counts
196 → 222
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0108218495
1393217678
2499717678
3494417678

prune1.3s (12%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New5322534
Fresh246
Picked011
Done011
Total5348542
Error
3.9b
Counts
542 → 8
Alt Table
StatusErrorProgram
26.5b
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
26.2b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))))
26.2b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
26.1b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
43.7b
(cbrt.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
4.6b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
37.2b
(*.f64 4 (*.f64 y t))
40.6b
(pow.f64 x 2)
Compiler

Compiled 48004 to 27666 computations (42.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
2.0b
(sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
2.5b
(cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
4.3b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series359.0ms (3.3%)

Counts
2 → 96
Calls

2 calls:

182.0ms
(cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))
177.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×pow1_binary64
sqrt-pow1_binary64
pow1/3_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
2 → 34
Calls

2 calls:

2.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
1.0ms
(cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))

simplify173.0ms (1.6%)

Algorithm
egg-herbie
Rules
412×times-frac_binary64
349×fma-def_binary64
333×associate-*l*_binary64
320×associate-/r*_binary64
290×associate-/l*_binary64
Counts
130 → 120
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047411944
1157211477
2509611477

prune1.3s (11.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New6150615
Fresh055
Picked011
Done022
Total6158623
Error
3.9b
Counts
623 → 8
Alt Table
StatusErrorProgram
26.5b
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
26.2b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))))
26.2b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))
26.1b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (sqrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))))
43.7b
(cbrt.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
4.6b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
37.2b
(*.f64 4 (*.f64 y t))
40.6b
(pow.f64 x 2)
Compiler

Compiled 68209 to 35371 computations (48.1% saved)

regimes2.8s (25.6%)

Accuracy

Total 1.0b remaining (16.5%)

Threshold costs 1.0b (16.5%)

Counts
209 → 1
Compiler

Compiled 94067 to 51158 computations (45.6% 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
01117
11717
22417
32817
43017
53017

end154.0ms (1.4%)

Compiler

Compiled 372 to 186 computations (50% saved)

Profiling

Loading profile data...